WITNESSETH:

Exhibit 4.3

FIRST SUPPLEMENTAL INDENTURE, dated as of October 31, 2013, among STERLING BANCORP, a corporation duly organized and existing under the laws of the State of New York (the “Company”), PROVIDENT NEW YORK BANCORP, a corporation duly organized and existing under the laws of the State of Delaware (the “Successor Company”), and THE BANK OF NEW YORK MELLON, formerly known as The Bank of New York, as Trustee under the Indenture referred to below (the “Trustee”).

WITNESSETH:

WHEREAS, the Trustee and the Company are parties to that certain Junior Subordinated Indenture, dated as of February 27, 2002 (the “Indenture”), providing for the issuance of Securities from time to time; and

WHEREAS, Section 8.1 of the Indenture provides that the Company shall not merge into another corporation unless, among other things, the corporation into which the Company is merged shall expressly assume, by an indenture supplemental to the Indenture, executed and delivered to the Trustee, in a form satisfactory to the Trustee, the due and punctual payment of the principal of and premium, if any, and interest (including any Additional Interest, as defined in the Indenture) on all the Securities of every series and the performance of every covenant of the Indenture on the part of the Company to be performed or observed; and

WHEREAS, Section 9.1 of the Indenture provides that the Company, when authorized by a Board Resolution, and the Trustee may enter into a supplemental indenture to evidence the succession of another Person to the Company and the assumption by any such successor of the covenants of the Company under the Indenture and in the Securities; and

WHEREAS, the Company and the Successor Company have entered into an Agreement and Plan of Merger, dated as of April 3, 2013 (the “Merger Agreement”), which contemplates the merger of the Company with and into the Successor Company (the “Merger”), with the Successor Company as the surviving corporation and continuing its corporate existence under the laws of the State of Delaware; and

WHEREAS, at the Effective Time (as defined below) the Successor Company will change its name to “Sterling Bancorp”; and

WHEREAS, the Company, pursuant to the foregoing authority, proposes in and by this First Supplemental Indenture to amend and supplement the Indenture in certain respects; and

WHEREAS, the Company has duly authorized the execution and delivery of this First Supplemental Indenture by a Board Resolution, as defined in the Indenture, and all things necessary to make this First Supplemental Indenture a valid agreement of the Successor Company, in accordance with the terms of the Indenture, have been done;

NOW, THEREFORE, for and in consideration of the premises and intending to be legally bound hereby, it is mutually covenanted and agreed, for the equal and proportionate benefit of all Holders, as follows:

ARTICLE ONE

REPRESENTATIONS OF THE COMPANY AND SUCCESSOR COMPANY

The Company and the Successor Company, respectively, represent to the Trustee as follows:

SECTION 1.1. The Company represents that it is a corporation duly organized, validly existing and in good standing under the laws of the State of New York.  The Successor Company represents that it is a corporation duly organized, validly existing and in good standing under the laws of the State of Delaware.

SECTION 1.2. The execution, delivery and performance by it of this First Supplemental Indenture has been authorized and approved by all necessary corporate action required to be taken by it.

SECTION 1.3. The Merger will become effective in accordance with the terms of the Merger Agreement as set forth in the certificate of merger to be filed in the office of the Secretary of State of Delaware and a certificate of merger to be filed in the office of the Department of State of New York (the time the Merger becomes effective being the “Effective Time”).

SECTION 1.4. Immediately after giving effect to the Merger, no Event of Default, and no event which, after notice or lapse of time or both, would constitute an Event of Default, shall have happened and be continuing.

ARTICLE TWO

ASSUMPTION AND AGREEMENTS

SECTION 2.1. The Successor Company hereby assumes, effective as of the Effective Time, the due and punctual payment of the principal of and any premium and interest (including any Additional Interest, as defined in the Indenture) on all the Securities of every series and the performance of every covenant of the Indenture on the part of the Company to be performed or observed.

SECTION 2.2. In accordance with Section 8.2 of the Indenture, effective as of the Effective Time, the Successor Company shall succeed to, and be substituted for, and may exercise every right and power of, the Company under the Indenture, with the same effect as if the Successor Company had been named as the Company therein, and the Company shall be discharged of all obligations and covenants under the Indenture and the Securities.

ARTICLE THREE

MISCELLANEOUS

SECTION 3.1. If any provision of this First Supplemental Indenture limits, qualifies or conflicts with the duties imposed by any of Sections 310 to 317, inclusive, of the Trust Indenture Act through operation of Section 318(c) thereof, such imposed duties shall control.

SECTION 3.2. Nothing in this First Supplemental Indenture, express or implied, shall give to any Person, other than the parties hereto and their successors and assigns any benefit or any legal or equitable right, remedy or claim under this First Supplemental Indenture.

SECTION 3.3.  All capitalized terms not otherwise defined herein shall have the meaning ascribed to them in the Indenture.

SECTION 3.4. This First Supplemental Indenture shall be governed by and construed in accordance with the laws of the State of New York, without regard to conflict of law principles thereof.

SECTION 3.5. This First Supplemental Indenture may be executed in any number of counterparts, each of which so executed shall be deemed to be an original, but all such counterparts shall together constitute but one and the same instrument.

SECTION 3.6. This First Supplemental Indenture shall become effective as of the Effective Time.

SECTION 3.7. The Trustee shall not be responsible in any manner whatsoever for or in respect of the validity or sufficiency of this First Supplemental Indenture.  The recitals of fact contained herein shall be taken as the statements solely of the Company or the Successor Company and the Trustee assumes no responsibility for the correctness thereof.

[The rest of this page intentionally left blank]

IN WITNESS WHEREOF, the parties hereto have caused this First Supplemental Indenture to be duly executed as of the day and year first above written.

[Signature Page to Supplemental Indenture]