Yep. That's why they have due process and fair trials in California. At least according to the CA and US high courts. Some people say that any execution is immoral, and there's a good argument there as well.
A trial that could lead to a death penalty can never be "fair" because this kind of punishment leaves no room for re-socialization of the convict. There are certain rights that no punishment could ever take away from a human being. At least we have them here, in the EU.