Exhibit 4.2

THIS FIRST SUPPLEMENTAL INDENTURE, dated as of April 1, 2013 (hereinafter called the “Supplemental Indenture”), is by and among UNITED CONTINENTAL HOLDINGS, INC. (formerly UAL Corporation), a Delaware corporation (hereinafter called the “Company”), as Issuer, UNITED AIRLINES, INC. (formerly Continental Airlines, Inc. (“Continental”)), a Delaware corporation and wholly owned subsidiary of the Company (hereinafter called the “Guarantor”), as Guarantor, and THE BANK OF NEW YORK MELLON TRUST COMPANY, N.A. (formerly The Bank of New York Trust Company, N.A.), a national banking association duly organized and existing under the laws of the United States of America, as trustee (hereinafter called the “Trustee”). Capitalized terms used but not defined herein are used as they are defined in the Original Indenture (as defined below).

RECITALS

A. The Company, United Air Lines, Inc., a Delaware corporation (“United”), as guarantor, and the Trustee entered into an Indenture, dated as of July 25, 2006 (the “Original Indenture”), relating to the issuance by the Company of 4.50% Senior Limited-Subordination Convertible Notes due 2021 (the “Notes”).

B. Continental and United entered into an Agreement and Plan of Merger, dated as of March 28, 2013, providing for the merger of United with and into Continental, with Continental, which changed its name to United Airlines, Inc. upon the effectiveness of such merger, continuing as the surviving corporation (the “Merger”).

C. The Company and the Guarantor have duly authorized the execution and delivery of this Supplemental Indenture.

D. Section 11.4 of the Original Indenture provides that the Original Indenture does not prohibit the Merger, provided that the Guarantor shall unconditionally assume all obligations of United under the Notes, the Original Indenture and the Note Guarantee pursuant to a supplemental indenture.

E. Section 8.1 of the Original Indenture permits the Company, the Guarantor and the Trustee to enter into the Supplemental Indenture without the consent of the holders of the Notes.

F. The Company has furnished the Trustee with an Opinion of Counsel complying with the requirements of Sections 1.2 and 1.3 of the Original Indenture, stating that the execution of this Supplemental Indenture is authorized or permitted by the Original Indenture.

G. All things necessary to make this Supplemental Indenture a valid agreement of the Company, the Guarantor 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, in consideration of the foregoing and for other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the Company, Guarantor and Trustee hereby agree as follows:

ARTICLE I

ASSUMPTION

Section 1.1 Assumption. The Guarantor hereby expressly assumes the due and punctual payment in full of the principal of and premium, if any, and interest on the Notes, and the due and punctual performance and observance of all of the covenants and conditions of the Original Indenture to be performed by United.

Section 1.2 Successor Guarantor. In accordance with Section 11.4 of the Original Indenture, the Guarantor hereby succeeds to and is substituted for United with the same effect as if the Guarantor had been named therein as the guarantor of the Notes.

ARTICLE II

MISCELLANEOUS

Section 2.1 Concerning the Trustee. 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 the Guarantor.

Section 2.2 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 2.3 Governing Law. THIS SUPPLEMENTAL INDENTURE SHALL BE GOVERNED BY AND CONSTRUED IN ACCORDANCE WITH THE LAWS OF THE STATE OF NEW YORK, WITHOUT REGARD TO PRINCIPLES OF CONFLICTS OF LAW.

Section 2.4 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. This Supplemental Indenture may be executed in any number of counterparts, each of which shall be an original, but such counterparts shall together constitute but one instrument.

Section 2.5 Ratification of Original Indenture. The Original Indenture, as amended and supplemented hereby, is in all respects hereby adopted, ratified and confirmed.

Section 2.6 Headings. 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.

Signature Page

Supplemental Indenture for 2021 Notes