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                                                                    EXHIBIT 4.13

                        AMENDMENT TO GUARANTEE AGREEMENT

                  This Amendment to Guarantee Agreement (the "Amendment") is
made as of December 23, 1999 by and between M&T Bank Corporation, a New York
corporation, and Bankers Trust Company, a New York banking corporation.

                                   WITNESSETH

                  WHEREAS, M&T Bank Corporation, formerly known as First Empire
State Corporation, (the "Guarantor"), and Bankers Trust Company, as trustee (in
such capacity, the "Guarantee Trustee") previously entered into a Guarantee
Agreement dated as of June 6, 1997 (the "Guarantee Agreement") by which the
Guarantor agreed to make certain payments to the Holders of Capital Securities
issued pursuant to an Amended and Restated Trust Agreement dated as of June 6,
1997 by and between Guarantor, in its capacity as Depositor, Bankers Trust
Company, as property trustee, and Bankers Trust (Delaware), a Delaware banking
corporation, as Delaware trustee; and

                  WHEREAS, the Guarantor has changed its corporate name from
"First Empire State Corporation" to "M&T Bank Corporation;" and

                  WHEREAS, the Administrators of the Issuer Trust have changed
the name of the Issuer Trust from "First Empire Capital Trust II" to "M&T
Capital Trust II;" and

                  WHEREAS, the Guarantor and the Guarantee Trustee desire to
amend the Guarantee Agreement to provide for the change of the name of the
Guarantor from "First Empire State Corporation" to "M&T Bank Corporation," and
the name of the Issuer Trust from "First Empire Capital Trust II" to "M&T
Capital Trust II."

                  NOW THEREFORE, in consideration of the agreements and
obligations set forth herein and for other good and valuable consideration, the
receipt and sufficiency of which are hereby acknowledged, each party to this
Amendment, for the benefit of the other parties and for the benefit of the
Holders, hereby amends the Guarantee Agreement, and agrees, intending to be
legally bound, as follows:

SECTION 1.  DEFINITIONS.

                  1.1. For all purposes of this Amendment, except as otherwise
expressly provided, terms used but not defined in this Amendment shall have the
meanings assigned to them in the Guarantee Agreement.

                  1.2. The definition of "Guarantor" in the preamble of the
Guarantee Agreement is amended to mean M&T Bank Corporation.


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                  1.3. The definition of "Issuer Trust" in the preamble of the
Guarantee Agreement is amended to mean "M&T Capital Trust II."

SECTION 2.  MISCELLANEOUS.

                  2.1. CONTINUING AGREEMENT. The Guarantee Agreement shall not
be amended by this Amendment except as specifically provided in this Amendment
and, amended as so specifically provided, the Guarantee Agreement shall remain
in full force and effect. References in the Guarantee Agreement to "this
Guarantee Agreement" shall be deemed to be references to the Guarantee Agreement
as amended by this Amendment.

                  2.2. CONFLICTS. In the event of a conflict between the terms
and conditions of the Guarantee Agreement and the terms and conditions of this
Amendment, the terms and conditions of this Amendment shall prevail.

                  2.3. COUNTERPART ORIGINALS. The parties may sign any number of
copies of this Amendment. Each signed copy shall be an original, but all of them
together represent the same agreement.

                  2.4. HEADINGS, ETC. The headings of the sections of this
Amendment have been inserted for convenience of reference only, are not to be
considered a part hereof, and shall in no way modify or restrict any of the
terms or provisions hereof.

                  IN WITNESS WHEREOF the parties have caused this Amendment to
be executed as of the day and year first above written.

                                              M&T BANK CORPORATION,
                                              as Guarantor

                                              By: /S/ MICHAEL P. PINTO
                                                 -------------------------------
                                              Michael P. Pinto
                                              Executive Vice President
                                              and Chief Financial Officer

                                              BANKERS TRUST COMPANY,
                                              as Guarantee Trustee,
                                              and not in its individual capacity

                                              By: /S/ CHRISTOPHER D. LEW
                                                 -------------------------------
                                              Christopher D. Lew
                                              Assistant Treasurer


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