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                                                                    Exhibit 10.4

                                    AGREEMENT

            AGREEMENT, dated as of January 30, 1998 between Dime Bancorp, Inc.,
a Delaware corporation having its principal executive offices at 589 Fifth
Avenue, New York, New York 10017 (the "Company"), and ANTHONY BURRIESCI (the
"Officer").

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            A. The Dime Savings Bank of New York, FSB (the "Bank"), a
wholly-owned subsidiary of the Company, has entered into an employment agreement
of even date herewith with the Officer (the "Employment Agreement"), and on July
1, 1997, an Agreement Regarding Initial Employment Terms with the Officer, with
an amendment thereto effective as of July 24, 1997 (together with such
amendment, the "Initial Terms Letter").

            B. The Company is desirous of having the Bank employ the Officer
upon the terms and conditions set forth in the Employment Agreement and the
Initial Terms Letter.

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            Therefore, the Company and the Officer, intending to be legally
bound, agree that the Company shall be jointly and severally liable with the
Bank with respect to any benefits or payments due under the Employment Agreement
and the Initial Terms Letter to the Officer, and the Company agrees to honor any
such obligations that are not fulfilled by the Bank.

                                        DIME BANCORP, INC.

                                        By:/s/LAWRENCE J. TOAL
                                           --------------------------
                                           Name:
                                           Title:
                                        /s/ANTHONY BURRIESCI
                                        -----------------------------
                                        ANTHONY BURRIESCI