The Bank of New York Company, Inc. [LOGO]

The Bank of New York Company, Inc.
$1,000,000,000
The Bank of New York Company, Inc. CoreNotes(Registered Service Mark)

            Filed under Rule 424 (b)(3), Registration Statement No. 333-103003,
                  333-103003-01, 333-103003-02, 333-103003-03 and 333-103003-04
                                 Pricing Supplement No. 36 - dated May 21, 2004
                                         (To prospectus dated March 6, 2003 and
                                    prospectus supplement dated March 28, 2003)
=================================================================
             Aggregate               Purchasing     Proceeds
  CUSIP      Principal   Price to      Agent's       Before
  Number      Amount     Public(1)   Discount(1)    Expenses(1)
=================================================================

06406JFR1   $1,772,000      100%         2.00%         98.00%

-----------------------------------------------------------------

=================================================================
   Interest      Interest        Stated
   Rate Per      Payment        Maturity     Survivor's
    Annum       Frequency         Date        Option
=================================================================

    5.90%      Semiannual       05/15/2019      YES

-----------------------------------------------------------------
Senior Subordinated Medium-Term Notes Series F
Interest Payment Dates:  The 15th day of May and November of each year
                         commencing 11/15/2004.
Redemption Information:  Redeemable at the option of The Bank of New York
                         Company, Inc. on 05/15/2007 and each Interest Payment
                         Date thereafter, at a price equal to 100% on 30
                         calendar days notice.
=================================================================
             Aggregate               Purchasing     Proceeds
  CUSIP      Principal   Price to      Agent's       Before
  Number      Amount     Public(1)   Discount(1)    Expenses(1)
=================================================================

06406JFS9   $2,821,000     100%         2.50%          97.50%

-----------------------------------------------------------------

=================================================================
   Interest      Interest        Stated
   Rate Per      Payment        Maturity     Survivor's
    Annum       Frequency         Date        Option
=================================================================

    6.00%      Semiannual      05/15/2029       YES

-----------------------------------------------------------------
Senior Subordinated Medium-Term Notes Series F
Interest Payment Dates:  The 15th day of May and November of each year
                         commencing 11/15/2004.
Redemption Information:  Redeemable at the option of The Bank of New York
                         Company, Inc. on 05/15/2009 and each Interest Payment
                         Date thereafter, at a price equal to 100% on 30
                         calendar days notice.

-----------------------------------------------------------------

The Bank of New York Company, Inc.
One Wall Street
New York, New York 10286

Trade Date:  05/21/2004
Issue Date:  05/26/2004
Minimum Denominations/Increments: $1,000/$1,000
Original Issue Discount: No
All trades settle without accrued interest and clear SDFS: DTC Book-Entry only
Merrill Lynch DTC Participant Number:  161

The defeasance and covenant defeasance provisions of the Senior Indenture and
the Senior Subordinated Indenture described under "Description of Senior Debt
Securities and Senior Subordinated Debt Securities - Defeasance and Covenant
Defeasance" in the Prospectus will apply to the Senior and Senior Subordinated
Notes respectively.

(1) Expressed as a percentage of the aggregate principal amount
"CoreNotes(Registered Service Mark)" is a registered service mark of Merrill
Lynch & Co., Inc.

                                                            Merrill Lynch & Co.
                                                               Purchasing Agent
                                                            Acting as Principal
===============================================================================