EXHIBIT 5.1

OPINION OF MARGARET A. TREESE, DEPUTY GENERAL COUNSEL AND SECRETARY

June 2, 2020

Ladies and Gentlemen:

I am Deputy General Counsel and Secretary of Teradata Corporation (the “Company”), and have been asked to render this opinion in connection with the Registration Statement on Form S-8 which the Company proposes to file with the U.S. Securities and Exchange Commission (the “SEC”) under the Securities Act of 1933, as amended, registering 2,235,000 shares of common stock, par value $.01 per share, of the Company (the “Shares”) which may be offered and sold by the Company pursuant to the Teradata New Employee Stock Inducement Plan, the Teradata Incentive Stock Purchase Plan, and the Performance-Based Restricted Share Unit Agreement (2022 Performance Period Award) Inducement Grant, the Restricted Share Unit Agreement (New Hire Grant) Inducement Grant and the Restricted Share Unit Agreement (Graded Vesting) Inducement Grant to be entered into with Stephen McMillan (collectively, the “Plans and Awards”).

I, or attorneys under my supervision, have examined originals, or copies of originals certified to my satisfaction, of such agreements, documents, certificates and other statements of government officials and corporate officers and representatives and have reviewed and discussed other papers and matters of fact and law as we have deemed relevant and necessary and on which I have relied as a basis for the following opinions. I have assumed the authenticity of all documents submitted as originals and the conformity with the original documents of any copies of such documents submitted for examination.

In this regard, I am of the opinion that:

1. The Company is a corporation duly organized, validly existing and in good standing under the laws of the State of Delaware.

2. All proper corporate proceedings have been taken so that any Shares to be offered and sold pursuant to the Plan which are of original issuance, upon sale and payment therefor in accordance with the Plans and Awards and the resolutions of the Board of Directors relating to the offering and sale of Shares thereunder, will be legally-issued, fully paid and nonassessable.

I hereby consent to the filing of this opinion with the SEC in connection with the Registration Statement referred to above. In giving such consent, I do not, however, admit that I come within the category of persons whose consent is required under Section 7 of the Securities Act of 1933, as amended, or the rules and regulations thereunder.

Very truly yours,

/s/ Margaret A. Treese

Margaret A. Treese

Deputy General Counsel and Secretary