EXHIBIT 32.2


    CERTIFICATION PURSUANT TO 18 U.S.C. SECTION 1350, AS ADOPTED PURSUANT TO
                  SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002


         In connection with the Quarterly Report of Gouverneur Bancorp Inc. (the
"Company") on Form 10-QSB for the period ending June 30, 2004 as filed with the
Securities and Exchange Commission on the date hereof (the "Report"), I, Robert
J. Twyman, Chief Financial Officer of the Company, certify, pursuant to 18
U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes -Oxley
Act of 2002, that:

         1.  The Report fully complies with the requirements of Section 13(a) or
             15(d) of the Securities Exchange Act of 1934; and

         2.  The information contained in the Report fairly presents, in all
             material respects, the financial condition and results of
             operations of the Company as of and for the period covered by the
             Report.


August 11, 2004                   By: /s/ ROBERT J. TWYMAN
                                      ------------------------------------------
                                      Robert J. Twyman
                                      Vice President and Chief Financial Officer

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