UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549


                                  SCHEDULE 13G

                    Under the Securities Exchange Act of 1934
                                (Amendment No. )*

                         UNITED THERAPEUTICS CORPORATION
 ------------------------------------------------------------------------------
                                (Name of Issuer)

                     Common Stock, $0.01 Par Value Per Share
 ------------------------------------------------------------------------------
                         (Title of Class of Securities)

                                    91307C102
                                    ---------
                                 (CUSIP Number)

                                 April 19, 2004
                                 --------------
                      (Date of Event which Requires Filing
                               of this Statement)



Check the appropriate box to designate the rule pursuant to which this Schedule
is filed:

            [  ]   Rule 13d-1(b)
            [X ]   Rule 13d-1(c)
            [  ]   Rule 13d-1(d)



*The remainder of this cover page shall be filled out for a reporting person's
initial filing on this form with respect to the subject class of securities, and
for any subsequent amendment containing information which would alter the
disclosures provided in a prior cover page.

The information required on the remainder of this cover page shall not be deemed
to be "filed" for the purpose of Section 18 of the Securities Exchange Act of
1934 ("Act") or otherwise subject to the liabilities of that section of the Act
but shall be subject to all other provisions of the Act (however, see the
Notes).


                                  Page 1 of 12



--------------------------                            --------------------------
CUSIP No. 91307C102                   13G             Page  2  of  12  Pages
          ---------                                        ---    ----
--------------------------                            --------------------------

--------------------------------------------------------------------------------
     1 NAME OF REPORTING PERSON
       I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

       S.A.C. Capital Advisors, LLC
--------------------------------------------------------------------------------
     2 CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*
                                                                        (a) [ ]

                                                                        (b) [X]
--------------------------------------------------------------------------------
     3 SEC USE ONLY

--------------------------------------------------------------------------------
     4 CITIZENSHIP OR PLACE OF ORGANIZATION

       Delaware
--------------------------------------------------------------------------------
                 5 SOLE VOTING POWER

                   0
               -----------------------------------------------------------------
NUMBER OF        6 SHARED VOTING POWER
SHARES
BENEFICIALLY       289,254 (see Item 4)
OWNED          -----------------------------------------------------------------
BY               7 SOLE DISPOSITIVE POWER
EACH
REPORTING          0
PERSON         -----------------------------------------------------------------
WITH             8 SHARED DISPOSITIVE POWER

                   289,254 (see Item 4)
--------------------------------------------------------------------------------
     9 AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

       289,254 (see Item 4)
--------------------------------------------------------------------------------
    10 CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES

       [ ]
--------------------------------------------------------------------------------
    11 PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)

       1.3% (see Item 4)
--------------------------------------------------------------------------------
    12 TYPE OF REPORTING PERSON*

       00
--------------------------------------------------------------------------------
                       *SEE INSTRUCTION BEFORE FILLING OUT




--------------------------                            --------------------------
CUSIP No. 91307C102                   13G             Page  3  of  12  Pages
          ---------                                        ---    ----
--------------------------                            --------------------------

--------------------------------------------------------------------------------
     1 NAME OF REPORTING PERSON
       I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

       S.A.C. Capital Management, LLC
--------------------------------------------------------------------------------
     2 CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*
                                                                        (a) [ ]

                                                                        (b) [X]
--------------------------------------------------------------------------------
     3 SEC USE ONLY

--------------------------------------------------------------------------------
     4 CITIZENSHIP OR PLACE OF ORGANIZATION

       Delaware
--------------------------------------------------------------------------------
                 5 SOLE VOTING POWER

                   0
              ------------------------------------------------------------------
NUMBER OF        6 SHARED VOTING POWER
SHARES
BENEFICIALLY       289,254 (see Item 4)
OWNED         ------------------------------------------------------------------
BY               7 SOLE DISPOSITIVE POWER
EACH
REPORTING          0
PERSON        ------------------------------------------------------------------
WITH             8 SHARED DISPOSITIVE POWER

                   289,254 (see Item 4)
--------------------------------------------------------------------------------
     9 AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

       289,254 (see Item 4)
--------------------------------------------------------------------------------
    10 CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES

       [ ]
--------------------------------------------------------------------------------
    11 PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)

       1.3% (see Item 4)
--------------------------------------------------------------------------------
    12 TYPE OF REPORTING PERSON*

       00
--------------------------------------------------------------------------------
                       *SEE INSTRUCTION BEFORE FILLING OUT




--------------------------                            --------------------------
CUSIP No. 91307C102                   13G             Page  4  of  12  Pages
          ---------                                        ---    ----
--------------------------                            --------------------------

--------------------------------------------------------------------------------
     1 NAME OF REPORTING PERSON
       I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

       S.A.C. Capital Associates, LLC
--------------------------------------------------------------------------------
     2 CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*
                                                                        (a) [ ]

                                                                        (b) [X]
--------------------------------------------------------------------------------
     3 SEC USE ONLY

--------------------------------------------------------------------------------
     4 CITIZENSHIP OR PLACE OF ORGANIZATION

       Anguilla, British West Indies
--------------------------------------------------------------------------------
                 5 SOLE VOTING POWER

                   0
              ------------------------------------------------------------------
NUMBER OF        6 SHARED VOTING POWER
SHARES
BENEFICIALLY       289,254 (see Item 4)
OWNED         ------------------------------------------------------------------
BY               7 SOLE DISPOSITIVE POWER
EACH
REPORTING          0
PERSON        ------------------------------------------------------------------
WITH             8 SHARED DISPOSITIVE POWER

                   289,254 (see Item 4)
--------------------------------------------------------------------------------
     9 AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

       289,254 (see Item 4)
--------------------------------------------------------------------------------
    10 CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES

       [ ]
--------------------------------------------------------------------------------
    11 PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)

       1.3% (see Item 4)
--------------------------------------------------------------------------------
    12 TYPE OF REPORTING PERSON*

       00
--------------------------------------------------------------------------------
                       *SEE INSTRUCTION BEFORE FILLING OUT

--------------------------                            --------------------------
CUSIP No. 91307C102                   13G             Page  5  of  12  Pages
          ---------                                        ---    ----
--------------------------                            --------------------------

--------------------------------------------------------------------------------
     1 NAME OF REPORTING PERSON
       I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

       Sigma Capital Management, LLC
--------------------------------------------------------------------------------
     2 CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*
                                                                        (a) [ ]

                                                                        (b) [X]
--------------------------------------------------------------------------------
     3 SEC USE ONLY

--------------------------------------------------------------------------------
     4 CITIZENSHIP OR PLACE OF ORGANIZATION

       Delaware
--------------------------------------------------------------------------------
                 5 SOLE VOTING POWER

                   0
              ------------------------------------------------------------------
NUMBER OF        6 SHARED VOTING POWER
SHARES
BENEFICIALLY       1,273,365 (see Item 4)
OWNED         ------------------------------------------------------------------
BY               7 SOLE DISPOSITIVE POWER
EACH
REPORTING          0
PERSON        ------------------------------------------------------------------
WITH             8 SHARED DISPOSITIVE POWER

                   1,273,365 (see Item 4)
--------------------------------------------------------------------------------
     9 AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

       1,273,365 (see Item 4)
--------------------------------------------------------------------------------
    10 CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES

       [ ]
--------------------------------------------------------------------------------
    11 PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)

       6.0% (see Item 4)
--------------------------------------------------------------------------------
    12 TYPE OF REPORTING PERSON*

       00
--------------------------------------------------------------------------------
                       *SEE INSTRUCTION BEFORE FILLING OUT





--------------------------                            --------------------------
CUSIP No. 91307C102                   13G             Page  6  of  12  Pages
          ---------                                        ---    ----
--------------------------                            --------------------------

--------------------------------------------------------------------------------
     1 NAME OF REPORTING PERSON
       I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

       Sigma Capital Associates, LLC
--------------------------------------------------------------------------------
     2 CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*
                                                                        (a) [ ]

                                                                        (b) [X]
--------------------------------------------------------------------------------
     3 SEC USE ONLY

--------------------------------------------------------------------------------
     4 CITIZENSHIP OR PLACE OF ORGANIZATION

       Anguilla, British West Indies
--------------------------------------------------------------------------------
                 5 SOLE VOTING POWER

                   0
              ------------------------------------------------------------------
NUMBER OF        6 SHARED VOTING POWER
SHARES
BENEFICIALLY       1,273,365 (see Item 4)
OWNED         ------------------------------------------------------------------
BY               7 SOLE DISPOSITIVE POWER
EACH
REPORTING          0
PERSON        ------------------------------------------------------------------
WITH             8 SHARED DISPOSITIVE POWER

                   1,273,365 (see Item 4)
--------------------------------------------------------------------------------
     9 AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

       1,273,365 (see Item 4)
--------------------------------------------------------------------------------
    10 CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES

       [ ]
--------------------------------------------------------------------------------
    11 PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)

       6.0% (see Item 4)
--------------------------------------------------------------------------------
    12 TYPE OF REPORTING PERSON*

       00
--------------------------------------------------------------------------------
                       *SEE INSTRUCTION BEFORE FILLING OUT

--------------------------                            --------------------------
CUSIP No. 91307C102                   13G             Page  7  of  12  Pages
          ---------                                        ---    ----
--------------------------                            --------------------------

--------------------------------------------------------------------------------
     1 NAME OF REPORTING PERSON
       I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

       Steven A. Cohen
--------------------------------------------------------------------------------
     2 CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*
                                                                        (a) [ ]

                                                                        (b) [X]
--------------------------------------------------------------------------------
     3 SEC USE ONLY

--------------------------------------------------------------------------------
     4 CITIZENSHIP OR PLACE OF ORGANIZATION

       United States
--------------------------------------------------------------------------------
                 5 SOLE VOTING POWER

                   0
              ------------------------------------------------------------------
NUMBER OF        6 SHARED VOTING POWER
SHARES
BENEFICIALLY       1,562,619 (see Item 4)
OWNED         ------------------------------------------------------------------
BY               7 SOLE DISPOSITIVE POWER
EACH
REPORTING          0
PERSON        ------------------------------------------------------------------
WITH             8 SHARED DISPOSITIVE POWER

                   1,562,619 (see Item 4)
--------------------------------------------------------------------------------
     9 AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

       1,562,619 (see Item 4)
--------------------------------------------------------------------------------
    10 CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES

       [ ]
--------------------------------------------------------------------------------
    11 PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)

       7.3% (see Item 4)
--------------------------------------------------------------------------------
    12 TYPE OF REPORTING PERSON*

       IN
--------------------------------------------------------------------------------
                       *SEE INSTRUCTION BEFORE FILLING OUT





Item 1(a)           Name of Issuer:
                    --------------

                    United Therapeutics Corporation

Item 1(b)           Address of Issuer's Principal Executive Offices:
                    -----------------------------------------------

                    1110 Spring Street
                    Silver Spring, ND  20910

Items 2(a)          Name of Person Filing:
                    ---------------------

                    This statement is filed by: (i) S.A.C. Capital Advisors,
                    LLC, ("SAC Capital Advisors") with respect to Shares
                    beneficially owned by S.A.C. Capital Associates, LLC ("SAC
                    Capital Associates"); (ii) S.A.C. Capital Management, LLC,
                    ("SAC Capital Management") with respect to Shares
                    beneficially owned by SAC Capital Associates; (iii) SAC
                    Capital Associates with respect to Shares beneficially owned
                    by it; (iv) Sigma Capital Management, LLC ("Sigma Capital
                    Management") with respect to Shares beneficially owned by
                    Sigma Capital Associates, LLC ("Sigma Capital Associates");
                    (v) Sigma Capital Associates with respect to Shares
                    beneficially owned by it; and (vi) Steven A. Cohen with
                    respect to Shares beneficially owned by SAC Capital
                    Advisors, SAC Capital Management, SAC Capital Associates,
                    Sigma Capital Management and Sigma Capital Associates.

Item 2(b)           Address of Principal Business Office:
                    ------------------------------------

                    The address of the principal business office of (i) SAC
                    Capital Advisors and Mr. Cohen is 72 Cummings Point Road,
                    Stamford, Connecticut 06902, (ii) SAC Capital Management and
                    Sigma Capital Management is 540 Madison Avenue, New York,
                    New York 10022, and (iii) SAC Capital Associates, and Sigma
                    Capital Associates is P.O. Box 58, Victoria House, The
                    Valley, Anguilla, British West Indies.

Item 2(c)           Citizenship:
                    -----------

                    SAC Capital Advisors, SAC Capital Management and Sigma
                    Capital Management are Delaware limited liability companies.
                    SAC Capital Associates, and Sigma Capital Associates are
                    Anguillan limited liability companies. Mr. Cohen is a United
                    States citizen.


                                  Page 8 of 12



Item 2(d)           Title of Class of Securities:
                    ----------------------------

                    Common Stock, par value $0.01 per share

Item 2(e)           CUSIP Number:
                    ------------

                    91307C102

Item 3              Not Applicable
                    --------------

Item 4              Ownership:
                    ---------

                    The percentages used herein are calculated based upon the
                    Shares issued and outstanding as of March 1, 2004 as
                    reported on the Company's annual report on Form 10-K filed
                    with the Securities and Exchange Commission by the Company
                    for the fiscal year ended December 31, 2003.

                    As of the close of business on April 27, 2004:

                    1. S.A.C. Capital Advisors, LLC
                    (a) Amount beneficially owned: 289,254
                    (b) Percent of class: 1.3%
                    (c)(i) Sole power to vote or direct the vote: -0-
                    (ii) Shared power to vote or direct the vote: 289,254
                    (iii) Sole power to dispose or direct the disposition: -0-
                    (iv) Shared power to dispose or direct the disposition:
                    289,254

                    2. S.A.C. Capital Management, LLC
                    (a) Amount beneficially owned: 289,254
                    (b) Percent of class: 1.3%
                    (c)(i) Sole power to vote or direct the vote: -0-
                    (ii) Shared power to vote or direct the vote: 289,254
                    (iii) Sole power to dispose or direct the disposition: -0-
                    (iv) Shared power to dispose or direct the disposition:
                    289,254

                    3. S.A.C. Capital Associates, LLC
                    (a) Amount beneficially owned: 289,254
                    (b) Percent of class: 1.3%
                    (c)(i) Sole power to vote or direct the vote: -0-
                    (ii) Shared power to vote or direct the vote: 289,254
                    (iii) Sole power to dispose or direct the disposition: -0-
                    (iv) Shared power to dispose or direct the disposition:
                    289,254


                                  Page 9 of 12



                    4. Sigma Capital Management, LLC
                    (a) Amount beneficially owned: 1,273,365
                    (b) Percent of class: 6.0%
                    (c)(i) Sole power to vote or direct the vote: 1,273,365
                    (ii) Shared power to vote or direct the vote: -0-
                    (iii) Sole power to dispose or direct the disposition: -0-
                    (iv) Shared power to dispose or direct the disposition:
                    1,273,365

                    5. Sigma Capital Associates, LLC
                    (a) Amount beneficially owned: 1,273,365
                    (b) Percent of class: 6.0%
                    (c)(i) Sole power to vote or direct the vote: -0-
                    (ii) Shared power to vote or direct the vote: 1,273,365
                    (iii) Sole power to dispose or direct the disposition: -0-
                    (iv) Shared power to dispose or direct the disposition:
                    1,273,365

                    6. Steven A. Cohen
                    (a) Amount beneficially owned: 1,562,619
                    (b) Percent of class: 7.3%
                    (c)(i) Sole power to vote or direct the vote: -0-
                    (ii) Shared power to vote or direct the vote: 1,562,619
                    (iii) Sole power to dispose or direct the disposition: -0-
                    (iv) Shared power to dispose or direct the disposition:
                    1,562,619

                    SAC Capital Advisors, SAC Capital Management, Sigma Capital
                    Management, and Mr. Cohen own directly no Shares. Pursuant
                    to investment agreements, each of SAC Capital Advisors and
                    SAC Capital Management share all investment and voting power
                    with respect to the securities held by SAC Capital
                    Associates. Pursuant to an investment management agreement,
                    Sigma Capital Management maintains investment and voting
                    power with respect to the securities held by Sigma Capital
                    Associates. Mr. Cohen controls each of SAC Capital Advisors,
                    SAC Capital Management and Sigma Capital Management. By
                    reason of the provisions of Rule 13D-3 of the Securities
                    Exchange Act of 1934, as amended, each of (i) SAC Capital
                    Advisors, SAC Capital Management and Mr. Cohen may be deemed
                    to own beneficially 289,254 shares (constituting
                    approximately 1.3% of the Shares outstanding) and (ii) Sigma
                    Capital Management and Mr. Cohen may be deemed to own
                    beneficially 1,273,365 shares (constituting approximately
                    6.0% of the Shares outstanding). Each of SAC Capital
                    Advisors, SAC Capital Management, Sigma Capital Management
                    and Mr. Cohen disclaim beneficial ownership of any of the
                    securities covered by this statement.


                                 Page 10 of 12



Item 5              Ownership of Five Percent or Less of a Class:
                    --------------------------------------------

                    If this statement is being filed to report the fact that as
                    of the date hereof the reporting person has ceased to be the
                    beneficial owner of more than five percent of the class of
                    securities, check the following.

Item 6              Ownership of More than Five Percent on Behalf of Another
                    --------------------------------------------------------
                    Person:
                    ------

                    Not Applicable

Item 7              Identification and Classification of the
                    ----------------------------------------
                    Subsidiary Which Acquired the Security Being
                    --------------------------------------------
                    Reported on By the Parent Holding Company:
                    -----------------------------------------

                    Not Applicable

Item 8              Identification and Classification of Members
                    ---------------------------------------------
                    of the Group:
                    ------------

                    Not Applicable

Item 9              Notice of Dissolution of Group:
                    ------------------------------

                    Not Applicable

Item 10             Certification:
                    -------------

     By signing below the signatory certifies that, to the best of his knowledge
and belief, the securities referred to above were not acquired and are not held
for the purpose of or with the effect of changing or influencing the control of
the issuer of the securities and were not acquired and are not held in
connection with or as a participant in any transaction having that purpose or
effect.


                                 Page 11 of 12



                                    SIGNATURE
                                    ---------

     After reasonable inquiry and to the best of my knowledge and belief, I
certify that the information set forth in this statement is true, complete and
correct.

Dated:  April 28, 2004

S.A.C. CAPITAL ADVISORS, LLC


By: /s/ Peter Nussbaum
   ---------------------------
Name:  Peter Nussbaum
Title:  Authorized Person

S.A.C. CAPITAL MANAGEMENT, LLC


By: /s/ Peter Nussbaum
   ---------------------------
Name:  Peter Nussbaum
Title:  Authorized Person

S.A.C. CAPITAL ASSOCIATES, LLC


By: /s/ Peter Nussbaum
   ---------------------------
Name:  Peter Nussbaum
Title:  Authorized Person

SIGMA CAPITAL MANAGEMENT, LLC


By: /s/ Peter Nussbaum
   ---------------------------
Name:  Peter Nussbaum
Title:  Authorized Person

SIGMA CAPITAL ASSOCIATES, LLC


By: /s/ Peter Nussbaum
   ---------------------------
Name:  Peter Nussbaum
Title:  Authorized Person

STEVEN A. COHEN


By: /s/ Peter Nussbaum
   ---------------------------
Name:  Peter Nussbaum
Title:  Authorized Person


                                 Page 12 of 12