Exhibit 3.1

Amendment to the Amended and Restated Bylaws of Hudson City Bancorp, Inc.,

amended and restated as of March 13, 2012

Article IV, Section 3 shall be amended and restated in its entirety as follows:

Section 3. Age Limitation of Directors. No member of the Board who has reached the age of 75 shall be eligible for re-election and no person shall be eligible for initial election as a director who is seventy years of age or more; provided, however, that the Board, upon recommendation of the Nominating and Governance Committee and by a resolution approved by a majority of the disinterested members of the Board, may exclude an incumbent director from such age limitation for a specified period of time and for a specified valid reason.