Exhibit 4.1

Execution Version

CONTINENTAL AIRLINES, INC.,

AS ISSUER,

TO

THE BANK OF NEW YORK MELLON TRUST COMPANY, N.A.,

AS TRUSTEE

FIRST SUPPLEMENTAL INDENTURE

DATED AS OF OCTOBER 1, 2010

SUPPLEMENTING AND AMENDING THE INDENTURE DATED AS OF JUNE 10, 2003

(5% Convertible Notes due 2023)

THIS FIRST SUPPLEMENTAL INDENTURE, dated as of October 1, 2010, (hereinafter called the “Supplemental Indenture”), is by and among CONTINENTAL AIRLINES, INC., a Delaware corporation (hereinafter called the “Company”), UNITED CONTINENTAL HOLDINGS, INC., a Delaware corporation (hereinafter called “UAL”) formerly known as UAL Corporation, and THE BANK OF NEW YORK MELLON TRUST COMPANY, N.A., a national banking association duly organized and existing under the laws of the United States of America, as successor to J.P. Morgan Trust Company, National Association, as successor to Bank One, N.A. (hereinafter called the “Trustee”).

WHEREAS, the Company and the Trustee are parties to an Indenture, dated as of June 10, 2003 (the “Original Indenture”), relating to the issuance by the Company of 5% Convertible Notes due 2023 (the “2023 Notes”);

WHEREAS, the Company is a party to that certain Agreement and Plan of Merger with UAL Corporation and JT Merger Sub Inc., dated as of May 2, 2010 (the “Merger Agreement”), whereby, at the effective time of the transactions contemplated therein (the “Effective Time”), JT Merger Sub Inc. was merged with and into the Company, each share of the Company’s Class B common stock, par value $0.01 per share, was converted into 1.05 shares of common stock, par value $0.01 per share, of UAL (the “UAL Common Stock”) and the Company is continuing as the surviving corporation and as a wholly-owned subsidiary of UAL (collectively referred to herein as the “Merger”);

WHEREAS, the Company and UAL have duly authorized the execution and delivery of this Supplemental Indenture;

WHEREAS, Section 10.09 of the Original Indenture provides that if the Company is a party to a merger or binding share exchange which reclassifies or changes its outstanding Common Stock, the Person obligated to deliver securities upon conversion of the 2023 Notes shall enter into a supplemental indenture;

WHEREAS, the Company has furnished the Trustee with an Officer’s Certificate and an Opinion of Counsel complying with the requirements of Section 9.06 of the Original Indenture, stating that the execution of this Supplemental Indenture is authorized or permitted by the Original Indenture;

WHEREAS, all things necessary to make this Supplemental Indenture a valid agreement of the Company, UAL and the Trustee and a valid amendment of, and supplement to, the Original Indenture have been done. The entry into this Supplemental Indenture by the parties hereto is in all respects authorized by the provisions of the Original Indenture;

NOW THEREFORE:

It is mutually covenanted and agreed, for the equal and proportionate benefit of all Holders of the 2023 Notes, as follows:

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ARTICLE I

RELATION TO ORIGINAL INDENTURE;

DEFINITIONS AND INCORPORATION BY REFERENCE

Section 1.1 Definitions. For all purposes of the Original Indenture and this Supplemental Indenture as they relate to the 2023 Notes, except as otherwise expressly provided or unless the context otherwise requires:

ARTICLE II

CONVERSION INTO COMMON STOCK OF UAL

Section 2.1 Effect of Merger. In accordance with Section 10.09 of the Original Indenture, from and after the Effective Time of the Merger, the Holder of a Security may convert it into the amount of UAL Common Stock which such Holder would have received upon consummation of the Merger if such Holder had converted the Security into Common Stock (as defined in the Original Indenture) immediately before the Effective Time of the Merger.

Section 2.2 Adjustments to Conversion Price. As and to the extent required by Section 10.09 of the Original Indenture, the above referenced conversion rights shall be subject to adjustment as a result of events occurring subsequent to the date hereof as nearly equivalent as may be practical to the adjustments provided for in Article X of the Original Indenture.

ARTICLE III

MISCELLANEOUS

Section 3.1 Concerning the Trustee; Force Majeure. The Trustee assumes no duties, responsibilities or liabilities by reason of this Supplemental Indenture other than as set forth in the Original Indenture. The Trustee shall not be responsible in any manner whatsoever for or in respect of the validity or sufficiency of this Supplemental Indenture or for or in respect of the recitals contained herein, all of which recitals are made solely by the Company and UAL.

In no event shall the Trustee be responsible or liable for any failure or delay in the performance of its obligations hereunder arising out of or caused by, directly or indirectly, forces beyond its control, including, without limitation, strikes, work stoppages, accidents, acts of war or terrorism, civil or military disturbances, nuclear or natural catastrophes or acts of God, and interruptions, loss or malfunctions of utilities, communications or computer (software and hardware) services; it being understood that the Trustee shall use reasonable efforts which are consistent with accepted practices in the banking industry to resume performance as soon as practicable under the circumstances.

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Section 3.2 Supplemental Indenture Controls. In the event of a conflict or inconsistency between the Original Indenture and this Supplemental Indenture, the provisions of this Supplemental Indenture shall control.

Section 3.3 Governing Law. THIS SUPPLEMENTAL INDENTURE SHALL BE GOVERNED BY AND CONSTRUED IN ACCORDANCE WITH THE LAWS OF THE STATE OF NEW YORK.

Section 3.4 Multiple Originals. The parties may sign any number of copies of this Supplemental Indenture. Each signed copy shall be an original, but all of them together represent the same agreement. One originally signed copy is enough to prove this Supplemental Indenture.

Section 3.5 Confirmation of Indenture. The Original Indenture, as supplemented and amended by this Supplemental Indenture, is in all respects hereby adopted, ratified and confirmed by the Company and the Trustee. UAL hereby agrees to be bound by the provisions of Section 2.1 and 2.2 of this Supplemental Indenture. For the avoidance of doubt, UAL does not assume any obligations of the Company under the Original Indenture, as supplemented and amended by this Supplemental Indenture, other than as expressly provided for in this Section 3.5.

Section 3.6 Headings and Table of Contents. The Article and Section headings herein are for convenience only and shall not affect the construction hereof.

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IN WITNESS WHEREOF, the undersigned, being duly authorized, have executed this Supplemental Indenture on behalf of the respective parties hereto as of the date first above written.

CAL Signature Page

First Supplemental Indenture for 2023 Notes

UAL Signature Page

First Supplemental Indenture for 2023 Notes

Trustee Signature Page

First Supplemental Indenture for 2023 Notes