Can you be arrested for killing someone after you were already tried for murdering them?

Here's the layout: Say you kidnap somebody, and then you're tried for their murder because you make yourself an obvious suspect. But throughout the trial, for lack of evidence, you are proven not guilty. So after you dodge that bullet, can you go out in public and literally kill him and not be tried because of double jeopardy? I'd like to know the technicalities because it seems like it would work.