Exhibit 5.4

[LETTERHEAD OF VEDDER PRICE P.C.]

November 24, 2009

United Air Lines, Inc.

UAL Corporation

77 West Wacker Drive

Chicago, Illinois 60601

Ladies and Gentlemen:

We are acting as special counsel for United Air Lines, Inc., a Delaware corporation (“United”), and UAL Corporation, a Delaware corporation (“UAL”), in connection with the offer and sale by United of $810,337,000 aggregate amount of pass through certificates, Series 2009-2 (the “Pass Through Certificates”) pursuant to a shelf Registration Statement on Form S-3, File No. 333-143865 (the “Registration Statement”) as filed with the Securities and Exchange Commission (the “SEC”) under the Securities Act of 1933, as amended (the “Securities Act”) and the related guarantee by UAL of the payment obligations under equipment notes issued by United underlying the Pass Through Certificates (the “Guarantee”). The Registration Statement includes a prospectus dated June 19, 2007 describing the Pass Through Certificates and Guarantee (the “Base Prospectus”), which Base Prospectus has been supplemented by a prospectus supplement dated November 16, 2009 (the “Prospectus Supplement,” the Base Prospectus, as so supplemented being referred to as the “Prospectus”). United and UAL have entered into an Underwriting Agreement dated November 16, 2009 (the “Underwriting Agreement”) with J.P. Morgan Securities Inc., Morgan Stanley & Co. Incorporated and Goldman, Sachs & Co. as representatives of the several underwriters named in Schedule II to the Underwriting Agreement pursuant to which the Pass Through Certificates will be sold. A copy of the Underwriting Agreement has been filed by the Company with the SEC on Form 8-K.

The Pass Through Certificates will be issued pursuant to a Pass Through Trust Agreement dated as of June 26, 2007 (the “Basic Pass Through Trust Agreement”) between United and Wilmington Trust Company, as trustee (the “Pass Through Trustee”) thereunder, a form of which has been filed as an exhibit to the Registration Statement, and Supplements thereto relating to the Pass Through Certificates (the “Trust Supplements”) between United and the Pass Through Trustee, forms of which have been filed by United with the SEC on a Form 8-K. We understand that the Pass Through Certificates will be sold or delivered in a manner set

United Air Lines, Inc.

UAL Corporation

November 24, 2009

Page 2

forth in the Registration Statement and the Prospectus. We have assumed that the Basic Pass Through Trust Agreement has been duly authorized, executed and delivered by the Pass Through Trustee.

In connection with the opinions expressed below, we have examined originals, or copies identified to our satisfaction, of such agreements, documents and certificates of governmental officials and corporate officers as we have deemed necessary or advisable as a basis for such opinions. We have also examined (i) the Restated Certificate of Incorporation of United, as currently in effect, (ii) the Amended and Restated By-laws of United, as currently in effect, (iii) the Restated Certificate of Incorporation of UAL, (iv) the Amended and Restated Bylaws of UAL, (v) the Basic Pass Through Trust Agreement, and (vi) the Trust Supplements in the forms filed with the SEC. Unless otherwise defined herein, capitalized terms used herein have the meanings assigned thereto in the Basic Pass Through Trust Agreement. In such examination, we have assumed the genuineness of all signatures and the authenticity of all documents submitted to us as originals and the conformity with the originals of all documents submitted to us as copies.

Based on the foregoing, it is our opinion that:

1. Each of United and UAL is validly existing as a corporation in good standing under the laws of the State of Delaware.

2. United has the corporate power and authority to execute, deliver and perform its obligations under the Basic Pass Through Trust Agreement and the Trust Supplements.

3. UAL has the corporate power and authority to execute, deliver and perform its obligations under the Guarantee.

4. With respect to the Pass Through Certificates, when (a) the Trust Supplements and the execution, authentication, issuance and delivery of the Pass Through Certificates shall have been duly authorized by all necessary corporate action of the Pass Through Trustee, (b) the Trust Supplements shall have been duly executed and delivered by United and the Pass Through Trustee, and (c) the Pass Through Certificates shall have been duly executed, authenticated, issued and delivered by United and the Pass Through Trustee and issued, sold and paid for as contemplated by each of the Registration Statement, the Prospectus, the Basic Pass Through Trust Agreement, the Trust Supplements and the Underwriting Agreement, (i) the Basic Pass Through Trust Agreement and Trust Supplements will constitute a valid and legally binding obligation of United, enforceable against United in accordance with its terms, and (ii) the Pass Through Certificates will be validly issued and will be entitled to the benefits of the Basic Pass Through Trust Agreement and Trust Supplements.

United Air Lines, Inc.

UAL Corporation

November 24, 2009

Page 3

5. With respect to the Guarantee, upon payment of the consideration therefore provided for in the Underwriting Agreement, the Guarantee will constitute a valid and legally binding obligation of UAL, enforceable against UAL in accordance with its terms.

Insofar as the foregoing opinions relate to the enforceability of any instrument, such enforceability is subject to (a) applicable bankruptcy, insolvency, reorganization, fraudulent conveyance, rehabilitation, moratorium, marshaling and other laws affecting the enforcement generally of creditors’ rights and remedies, and (b) general principles of equity (regardless of whether such enforceability is considered in a proceeding in equity or at law), applicable law relating to fiduciary duties, and judicial imposition of an implied covenant of good faith and fair dealing. No opinion is given herein as to the availability of specific performance or equitable relief of any kind.

In giving the foregoing opinions, we do not purport to be experts on, or to express any opinion herein concerning, any laws other than the laws of the State of New York, the corporate law of the State of Delaware and the federal law of the United States of America, in each case as in effect on the date hereof, except that we express no opinion with respect to (i) the laws, regulations or ordinances of any county, town or municipality or governmental subdivision or agency thereof, (ii) state securities or blue sky laws, or (iii) federal securities laws, including, without limitation, the Securities Act.

We hereby consent to the filing of this opinion as an exhibit to the Registration Statement and to the reference to us under the caption “Legal Matters” in the Prospectus. In giving this consent, we do not admit that we are within the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations thereunder.