Why isn't this double jepardy?

Philadelphia area residents have no doubt heard of the death of police officer William T. Barkley. They have also heard that his killer, William J. Barnes, has been charged with the murder. The surprising fact of the case is that the shooting that supposedly caused the death took place 41 years ago, and that Barnes already served 15 years in jail for the shooting.

The sad truth in this story is that the officer, Barkley, suffered paralysis from the shooting and had health problems the rest of his life. Still, I would have thought that justice was served when Barnes was convicted of the crime and served his time. The articles do not say what Barnes was convicted of so long ago, and so you can see how an overzealous prosecutor might pull out one of the many crimes that wasn't used 41 years ago, or the "new" one of murder and retry the case. Don't get me wrong, I think that if you commit a crime you should submit to justice and punishment for it, and it seems to me that that is what happened to Barnes. I have heard of charges moving from attempted murder to murder when a victim dies in the hospital days after the fact, but usually that happens long before a trial, conviction and serving a sentence. Barnes has already been denied bail for his "offense".

This is not the same as if they just discovered the murder from 41 years ago. Barnes is no great citizen, he has been in and out of jail his whole life until a recent "turnaround". All of that still seems irrelevant to the the fact that this really looks like double jeopardy. I am not a lawyer so I am sure I am missing an important point. The whole case looks like it will center around medical experts trying to prove or disprove that the infection that Barkley finally died from was a direct result of the injuries from 41 years ago. Shooting a police officer and 40 years of paraylsis are so emotionally charged that I don't expect a reasoned rational discussion of the facts. I would just like some lawyer to explain the basis for the murder charges.