Does perjured testimony have to be proven on a motion for a new trial?

Although the use of perjured testimony to obtain a conviction is improper, United States v. Agurs, 427 U.S. 97, 103, 96 S.Ct. 2392, 2397, 49 L.Ed.2d 342 (1976), the burden on the defendant is heavy to establish that perjured testimony was used. When presented as a motion for a new trial, before the defendant can prevail:

(1) It must appear from the motion that the evidence relied on is, in fact, newly discovered, i.e., discovered after trial; (2) the motion must allege facts from which the court may infer diligence on the part of the movant; (3) the evidence relied on must not be merely cumulative or impeaching; (4) must be material to the issues involved; and (5) must be such as, on a new trial, would probably produce an acquittal.

United States v. Steel, 759 F.2d 706, 713 (9th Cir.1985) (emphasis in original).