SECOND SUPPLEMENTAL INDENTURE dated as of October 20, 2006 by and between CINACALCET ROYALTY SUB LLC, a Delaware limited liability company, as issuer of the Notes,

Exhibit 4.1

SECOND SUPPLEMENTAL INDENTURE

dated as of October 20, 2006

by and between

CINACALCET ROYALTY SUB LLC,

a Delaware limited liability company,

as issuer of the Notes,

and

U.S. BANK NATIONAL ASSOCIATION,

as initial trustee of the Notes

(Second Supplemental Indenture to the Indenture, dated as of December 22, 2004, between

Cinacalcet Royalty Sub LLC and U.S. Bank National Association, as previously amended by the

Supplemental Indenture, dated as of February 5, 2005)

SECOND SUPPLEMENTAL INDENTURE

SECOND SUPPLEMENTAL INDENTURE, dated as of October 20, 2006 (this “Supplemental Indenture”), by and between CINACALCET ROYALTY SUB LLC, a Delaware limited liability company, as issuer of the Notes (the “Issuer”), and U.S. BANK NATIONAL ASSOCIATION, a national banking association, as initial trustee of the Notes (the “Trustee”), supplemental to the Indenture, dated as of December 22, 2004, as previously amended by the Supplemental Indenture, dated as of February 5, 2005 (the “Indenture”), made and entered into by and between the Issuer and the Trustee. Capitalized terms used but not defined herein have the same meanings assigned such terms in the Indenture.

RECITALS OF ISSUER

A. The Issuer and the Trustee are parties to the Indenture, providing for, among other things, the authentication, delivery and administration of the Issuer’s Secured 8% Notes due 2017 (the “Notes”).

B. The Issuer has proposed certain amendments to permit and facilitate the pledge by NPS Pharmaceuticals, Inc. (“NPS”) or one of its subsidiaries of the equity interests of Issuer in connection with any financings NPS or its subsidiary may enter into from time to time in the future.

C. The Issuer has received the consent of a majority of the Outstanding Principal Balance of the Notes to the amendments set forth below in accordance with Section 9.01 of the Indenture.

D. The Issuer has directed the Trustee to execute and deliver this Supplemental Indenture in accordance with the terms of the Indenture.

NOW, THEREFORE, IT IS HEREBY COVENANTED AND AGREED by and between the parties hereto as follows:

ARTICLE I

AMENDMENTS TO INDENTURE

Section 1.01 Amendments to Indenture. The Indenture is hereby amended as follows:

(a) Article VI of the Table of Contents of the Indenture is hereby amended by deleting “Section 6.12 Pledge Agreement” in its entirety and replacing it with “Section 6.12 Reserved.”

(b) Section 1.01 of the Indenture is hereby amended by:

(i) Deleting the definition of “Pledge Agreement” in its entirety;

(ii) Deleting the definition of “Pledged Equity” in its entirety;

(iii) Deleting the definition of “Related Documents” in its entirety and replacing it with the following:

“Related Documents” means the Purchase and Sale Agreement, the License Agreement, this Indenture and the Notes.;

(iv) Deleting the definition of “Secured Party” in its entirety; and

(v) Deleting the definition of “Security Interests” in its entirety and replacing it with the following:

“Security Interests” means the security interests granted or expressed to be granted in the Collateral pursuant to the Granting Clause herein.

(c) Section 4.03 of the Agreement is hereby amended by:

(i) Deleting the comma between “the Notes” and “this Indenture” in the fourth line of the introductory paragraph and replacing it with “or”; and

(ii) Deleting “or the Pledge Agreement” immediately following “this Indenture” in the fourth and fifth lines.

(d) Section 4.04 of the Agreement is hereby amended by deleting “, the Pledge Agreement” in the third line of the introductory paragraph.

(e) Section 5.02(a) of the Indenture is hereby deleted in its entirety and replaced with the following:

No Release of Obligations. Except as expressly permitted by this Indenture, the Issuer shall not take any action, whether orally or in writing, which would amend, modify, supplement, restate, cancel or terminate or discharge or prejudice the validity or effectiveness of this Indenture or the Purchase and Sale Agreement, or permit any party to any such document to be released from such obligations.

(f) Section 5.02(f) of the Indenture is hereby deleted in its entirety and replaced with the following:

Limitation on the Issuance, Delivery and Sale of Capital Stock. Except for any additional Stock issued to NPS, the Issuer shall not, directly or indirectly, issue, deliver or sell, or consent to issue, deliver or sell any actual, contingent, future or executory membership interests, limited liability company interests, beneficial interests or other equity or ownership interests (however designated, whether voting or non-voting); provided, however, that the transfer of all or a portion of the equity interests of the Issuer to another party shall not be deemed the issuance, delivery or sale of such interest if concurrently with such transfer the Issuer delivers to the Trustee an Officer’s Certificate and an Opinion of Counsel to the effect that such transfer does not impair in any respect the continuing lien of this Indenture in the Collateral. Additionally, the Issuer shall not accept any capital contributions after the Closing Date except for contributions by NPS of

funds deposited into the Capital Account, which may be used only as provided in Section 3.01(h).

(g) Section 6.12 of the Indenture is hereby deleted in its entirety and replaced with “Reserved.”

Section 1.02 Receipt by Trustee. In accordance with Section 9.04 of the Indenture, the parties acknowledge that the Trustee has received an Officer’s Certificate and an Opinion of Counsel as conclusive evidence that this Supplemental Indenture complies with the applicable requirements of the Indenture.

ARTICLE II

MISCELLANEOUS

Section 2.01 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. This Supplemental Indenture shall form a part of the Indenture for all purposes, and shall be read and construed together with the Indenture, and every Note heretofore or hereafter authenticated and delivered under the Indenture shall be bound thereby.

Section 2.02 Severability. In the event that any provision of this Supplemental Indenture or the application thereof to any party hereto or to any circumstance or in any jurisdiction governing this Supplemental Indenture shall, to any extent, be invalid or unenforceable under any applicable statute, regulation or rule of law, then such provision shall be deemed inoperative to the extent that it is invalid or unenforceable and the remainder of this Supplemental Indenture, and the application of any such invalid or unenforceable provision to the parties, jurisdictions or circumstances other than to whom or to which it is held invalid or unenforceable, shall not be affected thereby nor shall the same affect the validity or enforceability of this Supplemental Indenture.

Section 2.03 Governing Law. THIS SUPPLEMENTAL INDENTURE SHALL IN ALL RESPECTS BE GOVERNED BY, AND CONSTRUED IN ACCORDANCE WITH, THE LAW OF THE STATE OF NEW YORK, INCLUDING ALL MATTERS OF CONSTRUCTION, VALIDITY AND PERFORMANCE.

Section 2.04 Counterparts. This Supplemental Indenture may be executed in one or more counterparts by the parties hereto, and each such counterpart shall be considered an original and all such counterparts shall constitute one and the same instrument.

Section 2.05 Headings, Etc. The headings of the Articles and Sections of this Supplemental Indenture have been inserted for convenience of reference only, are not to be considered a part hereof and shall in no way modify or restrict any of the terms and provisions hereof.

Section 2.06 Benefits of Supplemental Indenture. Nothing in this Supplemental Indenture, expressed or implied, shall give any Person, other than the parties hereto, any Registrar and any Paying Agent, and their respective successors hereunder and the Holders, any benefit or any legal or equitable right, remedy or claim under this Supplemental Indenture or the Indenture.

Section 2.07 Acceptance by Trustee. The Trustee hereby accepts the modifications of the Indenture effected by this Supplemental Indenture.

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