AMENDMENTNO. 2 TO AGREEMENT AND PLAN OF MERGER

Exhibit 2.1

Execution Copy

AMENDMENT NO. 2 TO AGREEMENT AND PLAN OF MERGER

This Amendment No. 2 (this “Amendment”) to the Agreement and Plan of Merger, dated as of August 27, 2012 and amended by Amendment No. 1 to Agreement and Plan of Merger (“Amendment No. 1”), dated as of April 13, 2013 (as amended, the “Agreement”), is made and entered into as of December 16, 2013, by and among M&T Bank Corporation, a New York business corporation (“M&T”), Hudson City Bancorp, Inc., a Delaware corporation (“Hudson”), and Wilmington Trust Corporation, a Delaware corporation and direct, wholly owned Subsidiary of M&T (“Merger Sub”).

RECITALS

A. M&T, Hudson and Merger Sub are parties to the Agreement.

B. As provided in Section 9.2 of the Agreement, the parties may amend the terms of the Agreement by an instrument in writing, signed by the parties.

C. The parties hereto desire to enter into this Amendment upon the terms and conditions set forth herein.

D. All capitalized terms contained in this Amendment, but not specifically defined in this Amendment, shall have the meanings ascribed to such terms in the Agreement.

AGREEMENT

1. Amendment to Section 1.2. Section 1.2 of the Agreement is hereby amended and restated to provide in its entirety as follows:

Section 1.2 Closing. On the terms and subject to the conditions set forth in this Agreement, the closing of the Merger (the “Closing”) shall take place at 10:00 a.m., New York City time, at the offices of Sullivan & Cromwell LLP, counsel to Hudson, on a date to be specified by the parties, which date shall be no later than three Business Days after the satisfaction or waiver (subject to applicable law) of the latest to occur of the conditions set forth in Article VII (other than those conditions that by their nature are to be satisfied or waived at the Closing, but subject to the satisfaction or waiver of those conditions) or, if later, a date specified by Hudson to the minimum extent necessary to give effect to the procedures prescribed in Section 2.3, unless another date, time or place is agreed to in writing by M&T and Hudson. The date on which the Closing occurs is referred to in this Agreement as the “Closing Date.”

2. Amendment to Section 6.1. Section 6.1(d) of the Agreement is hereby amended by adding the following proviso to the end thereof:

provided, further, that the definition of Burdensome Condition shall be deemed to exclude any action or effect to the extent arising or resulting from or related to matters, circumstances or issues in existence on or before December 16, 2013, or otherwise arising or resulting from or required by the Written Agreement, dated as of June 17, 2013, by and among M&T, M&T Bank and the Federal Reserve Bank of New York and the matters and circumstances reflected therein.

3. Amendments to Section 8.1.

(a) Section 8.1(b)(ii) of the Agreement is hereby amended by replacing the reference to “January 31, 2014” with the words “December 31, 2014”.

(b) Section 8.1 is hereby amended by replacing the period at the end of clause (c) with “; or” and adding the following clause (d):

(d) by Hudson, at any time, if Hudson reasonably determines that M&T or M&T Bank is unlikely to be able to obtain the Requisite Regulatory Approvals in time to permit the Closing to occur on or prior to the Outside Date due to M&T’s or M&T Bank’s performance under the Written Agreement, dated as of June 17, 2013, by and among M&T, M&T Bank and the Federal Reserve Bank of New York.

(c) The last paragraph of Section 8.1 is hereby amended by replacing the words “clause (b) or (c)” with “clause (b), (c) or (d)”.

4. Access. Subject to the terms of Section 6.2 of the Agreement, M&T shall provide Hudson with access on a timely basis to all information requested by Hudson that is reasonably necessary for Hudson to assess M&T’s progress in obtaining the Requisite Regulatory Approvals.

5. Permitted Actions. Notwithstanding any provision of the Agreement (including Section 5.1(i) or 5.2) to the contrary, the parties hereby agree to the matters set forth on Annex A hereto. The parties shall reasonably cooperate with respect to such matters.

6. No Further Amendments. Except as expressly amended hereby, the Agreement is in all respects ratified and confirmed, and all the terms, conditions and provisions thereof shall remain in full force and effect. This Amendment is limited precisely as written and shall not be deemed to be an amendment to any other term or condition of the Agreement or any of the documents referred to therein.

7. Effect of Amendment. This Amendment shall form a part of the Agreement for all purposes, and each party thereto and hereto shall be bound hereby. From and after the execution of this Amendment by the parties hereto, any reference to the Agreement shall be deemed a reference to the Agreement as amended hereby.

8. Counterparts. This Amendment may be executed in two or more counterparts (including by facsimile or other electronic means), all of which shall be considered one and the same agreement and shall become effective when counterparts have been signed by each of the parties and delivered to the other party, it being understood that each party need not sign the same counterpart.

9. Severability. Whenever possible, each provision or portion of any provision of this Amendment shall be interpreted in such manner as to be effective and valid under applicable law, but if any provision or portion of any provision of this Amendment is held to be invalid, illegal or unenforceable in any respect under any applicable law or rule in any jurisdiction, such invalidity, illegality or unenforceability shall not affect any other provision or portion of any provision in such jurisdiction, and this Amendment shall be reformed, construed and enforced in such jurisdiction as if such invalid, illegal or unenforceable provision or portion of any provision had never been contained herein.

10. Governing Law. This Amendment and all disputes or controversies arising out of or relating to this Amendment or the transactions contemplated hereby shall be governed by, and construed

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in accordance with, the internal laws of the State of New York, without regard to the laws of any other jurisdiction that might be applied because of the conflicts of laws principles of the State of New York (provided that the DGCL, including the provisions governing the fiduciary duties of directors, shall govern as applicable).

11. Headings. The headings used in this Amendment are inserted for purposes of convenience of reference only and shall not limit or define the meaning of any provisions of this Amendment.

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IN WITNESS WHEREOF, the parties hereto have caused this Amendment to be executed by their duly authorized officers as of the date and year first above written.

[Signature page to Amendment No. 2 to Agreement and Plan of Merger]

Annex A