Is it legal to murder someone after you've already been tried and convicted for their murder?

There is a double-jeopardy law in the US which means you can't be tried for the same crime twice. So let's say a wife fakes her own death and frames her husband. He is arrested for it and sent to prison for 25 years. He serves his time and is released. Then he finds his wife and kills her in broad daylight in front of a dozen witnesses. Technically, he can't be tried in court for her murder because he went through that already. He was tried, convicted, and served 25 years in prison for this crime so he can't be tried for this crime again. The law against double-jeopardy means he will walk away a free man after murdering his wife. Is this true? If not, why?