Form of Equity Appreciation Instrument

Exhibit 4.1

Form of Equity Appreciation Instrument

THIS EQUITY APPRECIATION INSTRUMENT AND ANY OTHER SECURITIES ACQUIRED UPON THE EXERCISE HEREOF HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED, OR SECURITIES LAWS OF ANY STATE AND MAY NOT BE TRANSFERRED, SOLD OR OTHERWISE DISPOSED OF EXCEPT WHILE A REGISTRATION STATEMENT RELATING THERETO IS IN EFFECT UNDER SUCH ACT AND APPLICABLE STATE SECURITIES LAWS OR PURSUANT TO AN EXEMPTION FROM REGISTRATION UNDER SUCH ACT OR SUCH LAWS. THIS EQUITY APPRECIATION INSTRUMENT AND SUCH OTHER SECURITIES MAY BE TRANSFERRED ONLY IN COMPLIANCE WITH THE CONDITIONS SPECIFIED HEREIN.

EQUITY APPRECIATION INSTRUMENT

Issue Date: December 4, 2009

1. Definitions. Unless the context otherwise requires, when used herein the following terms shall have the meanings indicated.

“Average VWAP” means during any period, the arithmetic average of VWAP for each trading day during that period.

“Board” means the Board of Directors of the Company.

“Business Day” means any day except Saturday, Sunday or any day which shall be a legal holiday or a day on which banking institutions in the City and State of New York generally are authorized or required by law or other governmental actions to close.

“Company Unit” means the Company’s common stock, par value $0.01 per share.

“Company” means New York Community Bancorp, Inc., a Delaware corporation.

“Determination Price” means the Average VWAP of the Company Unit over the two New York Stock Exchange trading days immediately prior to the earliest date on which the Notice of Exercise is delivered, by facsimile or courier, to the Company as set forth in Section 3.

“Exercise Price” means the greater of the closing market price of the Company’s common stock on the New York Stock Exchange on December 4, 2009 and $12.00.

“Expiration Time” has the meaning given to it in Section 3.

“FDIC” means the Federal Deposit Insurance Corporation.

“Holder” has the meaning given to it in Section 2.

“Person” has the meaning given to it in Section 3(a)(9) of the Exchange Act and as used in Sections 13(d)(3) and 14(d)(2) of the Exchange Act.

“Purchase and Assumption Agreement” means the Purchase and Assumption Agreement between the Company and the FDIC, dated December 4, 2009.

“SEC” means the Securities and Exchange Commission.

“Subject Units” is defined in Section 2.

“Equity Appreciation Instrument” means this Equity Appreciation Instrument, issued to the Holder pursuant to the Purchase and Assumption Agreement.

“VWAP” means, for any day, the per share volume weighted average price of our Company Units on the New York Stock Exchange from 9:30 a.m. to 4:00 p.m., New York City

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time, on that day as displayed under the heading Bloomberg VWAP on Bloomberg Page NYB <equity> AQR (or its equivalent successor page if such page is not available) in respect of the period from the scheduled open of trading on the relevant trading day until the scheduled close of trading on the relevant trading day (or if such volume weighted average price is unavailable, the market price of one Company Unit on such trading day determined, using a volume weighted average method, by a nationally recognized investment banking firm retained by us for this purpose).

2. Number of Subject Units; Exercise Price. This certifies that, for value received, the FDIC or its registered assigns (the “Holder”) is entitled, upon the terms and subject to the conditions hereinafter set forth, to acquire from the Company, in whole or in part, up to an aggregate of 25,000,000 fully paid and nonassessable Company Units (the “Subject Units”) of the Company, at a purchase price equal to the Exercise Price per Subject Unit.

3. Exercise of Equity Appreciation Instrument; Term. To the extent permitted by applicable laws and regulations, the right to purchase the Subject Units represented by this Equity Appreciation Instrument is exercisable, in whole or in part, by the Holder, on any New York Stock Exchange trading day prior to 11:00 a.m., New York City time, on or after December 9, 2009, but in no event later than 11:00 a.m., New York City time, on December 23, 2009 (the “Expiration Time”), by (i) the facsimile transmission of a Notice of Exercise in the form attached hereto, duly completed and executed on behalf of the Holder, to (516)  ###-###-####, to be followed by the surrender of the Equity Appreciation Instrument and the original copy of the executed Notice of Exercise, such original documents to be delivered by overnight courier to the office of the Company at 615 Merrick Avenue, Westbury, New York (or such other office or agency of the Company in the United States as the Company may designate by notice in writing to the Holder at the address of the Holder appearing on the books of the Company), and (ii), at the election of the Company:

(1) payment of the Exercise Price for the Subject Units thereby purchased by having the Company withhold from issuance a number of Company Units otherwise issuable upon exercise of the Equity Appreciation Instrument equal in value to the aggregate Exercise Price as to which this Equity Appreciation Instrument is so exercised based on the Determination Price; or

(2) by payment by the Company to the Holder an amount of cash, by wire transfer of immediately available funds to an account designated by the FDIC no later than 5:00 p.m. New York City time on the next business day following receipt of the Notice of Exercise, equal to (i) the aggregate Determination Price of the Company Units issuable upon exercise of this Equity Appreciation Instrument, minus (ii) the aggregate Exercise Price as to which this Equity Appreciation Instrument is so exercised.

For the avoidance of doubt, if the Company elects to pay cash to the Holder as described under (2) above, no Subject Units will be issued to such Holder. If the Holder does not exercise this Equity Appreciation Instrument in its entirety, the Holder will be entitled to receive from the Company within a reasonable time, and in any event not exceeding three Business Days, a new equity appreciation instrument in substantially identical form for the purchase of that number of

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Company Units equal to the number of Subject Units subject to this Equity Appreciation Instrument minus the number of Subject Units as to which this Equity Appreciation Instrument is so exercised.

Notwithstanding anything in this Equity Appreciation Instrument to the contrary, the Holder hereby acknowledges and agrees that its exercise of this Equity Appreciation Instrument for Subject Units is subject to the condition that the Holder will have first obtained any applicable governmental or other approvals necessary to prevent such Holder from being in violation of any applicable law, rule or regulation.

4. Issuance of Subject Units; Authorization; Listing. For the avoidance of doubt, this Section 4 shall only apply in the case that the Company elects to settle this Equity Appreciation Instrument pursuant to Section 3(1) hereof. Certificates for Subject Units issued upon exercise of this Equity Appreciation Instrument will be issued in such name or names as the Holder may designate and will be delivered to such named Person or Persons within a reasonable time, not to exceed three Business Days after the date on which this Equity Appreciation Instrument has been duly exercised in accordance with the terms of this Equity Appreciation Instrument. Upon the request of the Holder, the Company and the Holder will mutually cooperate in good faith to cause the Subject Units to be eligible for book-entry issuance and to be issued in book-entry form. The Company hereby represents and warrants that any Subject Units issued upon the exercise of this Equity Appreciation Instrument in accordance with the provisions of this Equity Appreciation Instrument will be duly and validly authorized and issued, fully paid and nonassessable and free from all taxes, liens and charges (other than liens or charges created by the Holder or taxes in respect of any transfer occurring contemporaneously therewith). The Company agrees that the Subject Units so issued will be deemed to have been issued to the Holder as of the close of business on the date on which this Equity Appreciation Instrument and the Exercise Price are delivered to the Company in accordance with the terms of this Equity Appreciation Instrument, notwithstanding that the stock transfer books of the Company may then be closed or certificates representing such Subject Units may not be actually delivered on such date. The Company will at all times reserve and keep available out of its authorized but unissued common stock, par value $0.01 per share, solely for the purpose of providing for the exercise of this Equity Appreciation Instrument, the aggregate number of Company Units then issuable upon exercise of this Equity Appreciation Instrument. The Company will (i) procure, at its sole expense, the listing of the Subject Units and other securities issuable upon exercise of this Equity Appreciation Instrument, subject to issuance or notice of issuance on all stock exchanges on which the Company Units are then listed or traded and (ii) maintain the listing of such Subject Units after issuance. The Company will use commercially reasonable efforts to ensure that the Subject Units may be issued without violation of any applicable law or regulation or of any requirement of any securities exchange on which the Subject Units, as the case may be, are listed or traded.

5. No Fractional Subject Units or Scrip. No fractional Subject Units or scrip representing fractional Subject Units shall be issued upon any exercise of this Equity Appreciation Instrument. In lieu of any fractional Subject Unit to which the Holder would otherwise be entitled, the Holder shall be entitled to receive a cash payment equal to the Determination Price for such fractional Company Unit on the trading day immediately prior to the date on which this Equity Appreciation Instrument and the Notice of Exercise are delivered

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to the Company minus the Exercise Price for such fractional share. The Holder expressly waives the right to receive any fractional Subject Unit upon exercise of this Equity Appreciation Instrument.

6. No Rights as Shareholders; Transfer Books. This Equity Appreciation Instrument does not entitle the Holder to any voting rights or other rights as a shareholder of the Company prior to the date of exercise hereof. The Company will at no time close its transfer books against transfer of this Equity Appreciation Instrument in any manner which interferes with the timely exercise of this Equity Appreciation Instrument.

7. Charges, Taxes and Expenses. Issuance of certificates for Subject Units to the Holder upon the exercise of this Equity Appreciation Instrument shall be made without charge to the Holder for any issue or transfer tax or other incidental expense in respect of the issuance of such certificates, all of which taxes and expenses shall be paid by the Company.

8. Transfer/Assignment. This Equity Appreciation Instrument and all rights hereunder are not transferable, in whole or in part, without the prior written consent of the Company, such consent not to be unreasonably withheld.

9. Exchange and Registry of Equity Appreciation Instrument. The Company shall maintain a registry showing the name and address of the Holder as the registered holder of this Equity Appreciation Instrument. This Equity Appreciation Instrument may be surrendered for exchange or exercise, in accordance with its terms, at the office of the Company, and the Company shall be entitled to rely in all respects, prior to written notice to the contrary, upon such registry.

10. Saturdays, Sundays, Holidays, etc. If the last or appointed day for the taking of any action or the expiration of any right required or granted herein shall not be a Business Day, then such action may be taken or such right may be exercised on the next succeeding day that is a Business Day.

11. Governing Law. This Equity Appreciation Instrument shall be binding upon any successors or assigns of the Company. This Equity Appreciation Instrument shall be governed by and construed in accordance with the federal law of the United States if and to the extent such law is applicable, and, insofar as there may be no applicable federal law, shall be governed in accordance with the laws of the State of New York applicable to contracts made and to be performed entirely within such state. Each of the Company and the Holder agrees (a) to submit to the exclusive jurisdiction and venue of the federal courts located in the Southern District of New York for any action, suit or proceeding arising out of or relating to this Equity Appreciation Instrument or the transactions contemplated hereby, and (b) that notice may be served upon the Company at the address in Section 16 below and upon the Holder at the address for the Holder set forth in the registry maintained by the Company pursuant to Section 9 hereof. To the extent permitted by applicable law, each of the Company and the Holder hereby unconditionally waives trial by jury in any legal action or proceeding relating to the Equity Appreciation Instrument or the transaction contemplated hereby or thereby.

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12. Amendments. This Equity Appreciation Instrument may be amended and the observance of any term of this Equity Appreciation Instrument may be waived only, in the case of an amendment, with the written consent of the Company and the Holder, or in the case of a waiver, by the party against whom the waiver is to be effective.

13. Notices. All notices hereunder shall be in writing and shall be effective (A) on the day on which delivered if delivered personally or transmitted by telex or telegram or telecopier with evidence of receipt, (B) one Business Day after the date on which the same is delivered to a nationally recognized overnight courier service with evidence of receipt, or (C) five Business Days after the date on which the same is deposited, postage prepaid, in the U.S. mail, sent by certified or registered mail, return receipt requested, and addressed to the party to be notified at the address indicated below for the Company, or at the address for the Holder set forth in the registry maintained by the Company pursuant to Section 9, or at such other address and/or telecopy or telex number and/or to the attention of such other person as the Company or the Holder may designate by ten-day advance written notice.

If to the Company, to:

New York Community Bancorp, Inc.

615 Merrick Avenue

Westbury, New York 11554

Attn: R. Patrick Quinn

Executive Vice President,

Chief Corporate Governance Officer and Corporate Secretary

Facsimile: (516)  ###-###-####

with a copy to (which copy alone shall not constitute notice):

Sullivan & Cromwell LLP

125 Broad Street

New York, New York 10004

Attn: Mark J. Menting

Andrew R. Gladin

Facsimile: (212)  ###-###-####

14. Entire Agreement. This Equity Appreciation Instrument and the forms attached hereto, and the Purchase and Assumption Agreement, contain the entire agreement between the parties with respect to the subject matter hereof and supersede all prior and contemporaneous arrangements or undertakings with respect thereto.

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IN WITNESS WHEREOF, the Company has caused this Equity Appreciation Instrument to be executed by a duly authorized officer as of the Issue Date written above.

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[Form Of Notice Of Exercise]

Date:                                         

The undersigned, pursuant to the provisions set forth in the attached Equity Appreciation Instrument, hereby agrees to exercise the Equity Appreciation Instrument with respect to the number of Company Units set forth below in accordance with Sections 2 and 3 thereof. A new equity appreciation instrument evidencing the remaining number of Company Units covered by such Equity Appreciation Instrument, but with respect to which the Holder has not yet exercised such Equity Adjustment Instrument, will be issued to the Holder.