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 March 31, 2005 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.


May 11, 2005                           By: /s/ ROBERT J. TWYMAN
                                           -------------------------------------
                                           Robert J. Twyman
                                           Vice President and Chief Financial
                                           Officer

         The foregoing certification is being furnished solely pursuant to
Subsections (a) and (b) of Section 1350, Chapter 63 of Title 18, United States
Code in accordance with Section 906 of the Sarbanes-Oxley Act of 2002 and shall
not be deemed "filed" for purposes of Section 18 of the Securities Exchange Act
of 1934, or otherwise subject to the liability of that section, and shall not be
deemed to be incorporated by reference into any filing under the Securities Act
of 1933 of the Securities Exchange Act of 1934.

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