While all murder is killing, not all killing is murder. Murder is killing with no moral justification. Murder is distinct from execution and euthanasia. Execution is the killing if someone both as a form if punishment and to remove a dangerous person from the population, the second reason being the most important. When someone is sentenced to death in the U.S. the murder must have included "special circumstances" which would indicated the individual was likely to murder again, if given the chance. As administered in the U.S. the death penalty is ineffective. We wait so song to administer it that it is no more effective than incarceration (with theoretical opportunities to escape and murder again). Also while someone who we've essentially acknowledged is unsalvageable is incarcerated, we waste resources on a person who will never benefit society and has proven detrimental to it.
So definitely think the penalty is supportable, but as used fails to serve it's purposes of removing a dangerous individual from the population and conserving resources.