Even before the law was changed you could still be tried for murder. This is why, the first murder the state accept now that you did not do and your senetence was served in error, the state is very sorry and would no doubt be compensated. Now the new murder is a completely seperate incident and is unrelated to the first, it is premeditated murder based on a false belief, you are nicked sunshine!
The file mentioned above falsely represented the double jeopardy rule, ie if you are tried for a crime and acquited then you cannot be retried for the same crime even if new evidence comes to light, that of course has now changed but the position you are referring to is clear.