BANKUNITED FINANCIAL CORPORATION

Exhibit 4.1

BANKUNITED FINANCIAL CORPORATION

$120,000,000

3.125% Convertible Senior Notes due 2034

FIRST SUPPLEMENTAL INDENTURE

Dated as of December 28, 2004

to

INDENTURE

Dated as of February 27, 2004

U.S. BANK NATIONAL ASSOCIATION

as Trustee

FIRST SUPPLEMENTAL INDENTURE, effective as of December 28, 2004 (this “First Supplemental Indenture”), to that certain Indenture, dated as of February 27, 2004 (the “Indenture”) between BANKUNITED FINANCIAL CORPORATION, a Florida Corporation (the “Company”), and U.S. BANK NATIONAL ASSOCIATION, a national banking association duly organized and existing under the laws of the United States as trustee (the “Trustee”). All terms used herein and not otherwise defined herein shall have the same respective meanings as in the Indenture.

R E C I T A L S:

A. The Company has heretofore executed and delivered the Indenture providing for the issuance of 3.125% Convertible Senior Notes due 2034 (the “Securities”);

B. Section 11.1 of the Indenture provides that the Company and the Trustee may amend the Indenture or the Securities without the consent of any Holder in a number of circumstances, including, without limitation, (i) to surrender any right or power conferred upon the Company by the Indenture, (ii) to cure any ambiguity, correct or supplement any provision of the Indenture which may be inconsistent with any other provision or which is otherwise defective, or to make any other provisions with respect to matters or questions arising under the Indenture which the Company may deem necessary or desirable and which shall not be inconsistent with the provisions of the Indenture; provided, that such action does not adversely affect the interests of the Holders; and (iii) to add or modify any other provisions of the Indenture with respect to matters or questions arising hereunder which the Company and the Trustee may deem necessary or desirable and which would not adversely affect the interests of the Holders;

C. Section 12.1 of the Indenture provides that the Holders shall have the right to convert all or any portion of the Securities into shares of the Company’s Class A Common Stock if certain specified conditions are met;

D. Section 12.2 of the Indenture provides that on the first date the Securities become so convertible, the Company shall make an election at its sole and absolute discretion, and notify the Holders in writing thereof, as to the amount of (x) Class A Common Stock, (y) Cash in lieu of Class A Common Stock, or (z) the combination of Cash and Class A Common Stock, the Company shall pay in settlement of the Principal Amounts at Issuance of the Securities upon conversion thereof;

E. Section 12.2 of the Indenture provides further that this notification, once provided to a Holder on the date the Securities first become convertible, is irrevocable and legally binding with regard to any conversion of the Securities;

F. The Company desires and has requested the Trustee to join the Company in the execution and delivery of this First Supplemental Indenture for the purpose of amending the Indenture to provide for the settlement of the Principal Amounts at Issuance solely in Cash; and

G. All things necessary to make this First Supplemental Indenture a valid and binding agreement of the Company and the Trustee and a valid and binding amendment of the Indenture have been done.

Each party agrees as follows for the benefit of the other party and for the equal and ratable benefit of the Holders of the Securities:

Section 1. Amendment.

(a) The second full paragraph of Section 12.2(a) of Article 12 of the Indenture is hereby amended and restated in its entirety by replacing it with the following language:

“Notwithstanding anything herein to the contrary, the Company shall satisfy its obligations to convert any Security surrendered by a Holder (each, a “Surrendered Security”), in respect of the Principal Amount at Issuance of such Security upon surrender thereof, entirely in Cash (the “Principal Conversion Settlement Election”). The aforementioned obligation to satisfy the Principal Amount at Issuance entirely in Cash shall be irrevocable.”

(b) All provisions of this Indenture and the Securities shall be read to give effect to the election in clause (a) of this Section above.

Section 2. Ratification of Indenture; Supplemental Indenture Part of Indenture. Except as expressly amended hereby, the Indenture is in all respects ratified and confirmed and all the terms, conditions and provisions thereof shall remain in full force and effect. In the event of a conflict between the terms and conditions of the Indenture and the terms and conditions of this First Supplemental Indenture, then the terms and conditions of this First Supplemental Indenture shall prevail. This First Supplemental Indenture shall form a part of the Indenture for all purposes, and every Security heretofore and hereafter authenticated and delivered shall be bound hereby.

Section 4. Governing Law. This First Supplemental Indenture shall be governed by, and construed in accordance with, the laws of the State of New York.

Section 5. Counterparts. The parties may sign any number of copies of this First Supplemental Indenture. Each signed copy shall be an original, but all of them together represent the same agreement. One signed copy is enough to prove this First Supplemental Indenture.

Section 6. Effect of Headings. The section headings herein are for convenience only and shall not affect the construction hereof.

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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.