Three-Month Periods Ended

Exhibit 10.5

SUPPLEMENTAL INDENTURE

SUPPLEMENTAL INDENTURE (this “Supplemental Indenture”), dated as of May 9, 2008, between Celgene Corporation, a Delaware corporation (the “Company”), and The Bank of New York, as trustee under the Indenture referred to below (the “Trustee”).

W I T N E S S E T H

WHEREAS, the Company has heretofore executed and delivered to the Trustee an indenture (as amended, supplemented or otherwise modified, the “Indenture”), dated as of June 3, 2003, providing for the issuance of $400,000,000 principal amount of the Company’s 1³/4% Convertible Notes due 2008 (the “Notes”); and

WHEREAS, pursuant to Section 2.03 of the Indenture, the interest due on June 1, 2008 (the “2008 Interest Payment Date”) is payable to the persons in whose name any Note is registered on the Note Register at the close of business on May 15, 2008 (the “2008 Record Date”); and

WHEREAS, pursuant to Section 16.01 of the Indenture, the holder of any Note may, at such holder’s option, convert the principal amount of such Note, or any portion of such principal amount which is a multiple of $1,000, into fully paid and non-assessable shares of Common Stock at any time prior to the close of business on June 1, 2008, the date that is the maturity date of the Notes; and

WHEREAS, pursuant to Section 16.02(c) of the Indenture, any Note or portion thereof surrendered for conversion during the period from the close of business on the 2008 Record Date to the close of business on the Business Day (as that term is defined in the Indenture) preceding the 2008 Interest Payment Date, i.e., May 30, 2008 (the “Section 16.02 Period”) shall be accompanied by payment, in immediately available funds or other funds acceptable to the Company, of an amount equal to the interest otherwise payable on such interest payment date on the principal amount being converted (the “Interest Amount”); and

WHEREAS, because June 1, 2008, the date that is the 2008 Interest Payment Date and the maturity date of the Notes, is not a Business Day, a holder of any Note cannot effect conversion of such Note after the Section 16.02 Period and prior to the close of business on the maturity date of the Notes in accordance with the requirements set forth in Section 16.02 of the Indenture, and thereby avoid the requirement to pay the Interest Amount upon such conversion; and

WHEREAS, pursuant to Section 12.01(f) of the Indenture provides that the Company, when authorized by resolutions of the Board of Directors of the Company, and the Trustee may, from time to time, and at any time enter into an indenture or indentures supplemental to the Indenture to, among other purposes, cure any ambiguity or to correct or supplement any provision contained herein or in any supplemental indenture that may be defective or inconsistent with any other provision contained in the Indenture or to make such other provisions in regard to matters or questions arising under the Indenture that shall not adversely affect the interests of the holders of the Notes; and

WHEREAS, for the sole purpose of permitting any holder of a Note to exercise the conversion privilege in accordance with the requirements set forth in Section 16.02 of the Indenture, as if the 2008 Interest Payment Date was a Business Day, and thereby avoid the requirement to pay the Interest Amount upon such conversion, the Company desires to supplement the Indenture to provide that for purposes of Section 16.02(c) of the Indenture, any Note or portion thereof surrendered for conversion after the close of business on May 29, 2008 and prior to the close of business on June 1, 2008 shall be deemed to have been surrendered for conversion after the Section 16.02 Period and, accordingly any such Note or portion thereof so surrendered for conversion need not be accompanied by payment of the Interest Amount;

NOW, THEREFORE, in order to supplement the terms and conditions upon which the Notes were authenticated, issued and delivered, and in consideration of the premises and of the purchase and acceptance of the Notes by the holders thereof, the Company covenants and agrees with the Trustee for the equal and proportionate benefit of the respective holders from time to time of the Notes (except as otherwise provided in the Indenture), as follows:

1. DEFINED TERMS. Capitalized terms that are not defined in this Supplemental Indenture shall have the meanings ascribed to such terms in the Indenture.

2. SECTION 16.02(c). Notwithstanding anything to the contrary contained in the Indenture, for purposes of Section 16.02(c) of the Indenture, any Note or portion thereof surrendered for conversion after the close of business on May 29, 2008 and prior to the close of business on June 1, 2008 shall be deemed to have been surrendered for conversion after the Section 16.02 Period and, accordingly any such Note or portion thereof so surrendered for conversion need not be accompanied by payment of the Interest Amount.

3. RATIFICATION OF INDENTURE; SUPPLEMENTAL INDENTURES 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. This Supplemental Indenture shall form a part of the Indenture for all purposes, and every holder of Notes heretofore or hereafter authenticated and delivered shall be bound hereby.

4. COUNTERPARTS. This Supplemental Indenture may be executed in any number of counterparts, but such counterparts together shall constitute but one and the same instrument.

5. EFFECT OF HEADINGS. The Section headings of this Supplemental Indenture have been inserted for convenience of reference only, are not considered a part hereof, and shall in no way modify or restrict any of the terms or provisions hereof.

6. GOVERNING LAW. This Supplemental Indenture shall be deemed to be a contract made under the laws of the State of New York, and for all purposes shall be construed in accordance with the laws of the State of New York, without regard to conflicts of laws principles thereof.

7. NO RESPONSIBILITY FOR RECITALS, ETC. The recitals contained herein shall be taken as the statements of the Company, and the Trustee assumes no responsibility for the correctness of the same. The Trustee makes no representations as to the validity or sufficiency of this Supplemental Indenture.

IN WITNESS WHEREOF, the parties hereto have caused this Supplemental Indenture to be duly executed and attested, all as of the date first above written.