When a conviction is vacated (as was the case here) it does not violate the double jeopardy clause to try the accused again for the charge for which he was convicted.
The case on point is United States v. Ball, 163 U.S. 662 (1896)* which rejects the English common law rule that holds the opposite. Frankfurter's dissent in Green v. United States, 355 U.S. 184 (1957)+ is far easier to read and lays out the history well.