Exhibit 13.2

CERTIFICATION PURSUANT TO

18 U.S.C. SECTION 1350

AS ADOPTED PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

In connection with the Annual Report of Alterity Therapeutics Limited (the “Company”) on Form 20-F for the year ended June 30, 2022, as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, Kathryn Andrews, Chief Financial Officer of the Company, certify, pursuant to 18 U.S.C. § 1350, as adopted pursuant to § 906 of the Sarbanes-Oxley Act of 2002, that:

(1) The Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

(2) The information contained in the Report fairly presents, in all material respects, the financial condition and result of operations of the Company.

August 31, 2022

/s/ Kathryn Andrews

Kathryn Andrews

Chief Financial Officer

* The originally executed copy of this Certification will be maintained at the Company’s offices and will be made available for inspection upon request.