It is, basically, but that's not really what the Double Jeopardy Clause was intended to prevent. Alexander Hamilton actually submitted slightly different language to the House:

No person shall be subject, except in cases of impeachment, to more than one punishment or trial for the same offense.

This was rejected due to fears that it could mean that a successful appeal, such as the one in McDonnell's case, would prevent a new trial. In other words, the Founders specifically decided that they didn't want the Double Jeopardy Clause to mean that there was literally only one shot at the prize for the prosecution. Instead, the idea was to prevent sour grapes (basically), i.e. the prosecution loses a case via acquittal, so they decide to try the person again.

“The constitutional prohibition against ‘double jeopardy’ was designed to protect an individual from being subjected to the hazards of trial and possible conviction more than once for an alleged offense. . . . The underlying idea, one that is deeply ingrained in at least the Anglo–American system of jurisprudence, is that the State with all its resources and power should not be allowed to make repeated attempts to convict an individual for an alleged offense, thereby subjecting him to embarrassment, expense and ordeal and compelling him to live in a continuing state of anxiety and insecurity, as well as enhancing the possibility that even though innocent he may be found guilty.”

Green v. United States, 355 U.S. 184, 187–88 (1957). This desire isn't thwarted if it's the defendant who appeals his conviction. In other words, he asked for it. This isn't to say the prosecution can never appeal in a criminal case, but usually that gets more into collateral issues and not the underlying guilt or innocence. See, for example, a rather disturbing case (in more ways than one) from earlier in this term where the prosecution appealed a state supreme court's decision to vacate a sentence of death. The lone dissenting justice on the US Supreme Court argued (persuasively in my opinion) that the case never should've been heard, although not on Double Jeopardy grounds.