I believe you are mistaken. The Bible is full of stories of people who murdered others, including King David. Yet he was one of God's favorites.
Even on the cross, Jesus asked God to forgive his murderers. I don't think he would have asked if it were impossible.
Others have mentioned Paul's role in the murder of Stephen and others.
I'm not familiar with any scripture that says or even implies that murder is unforgivable. If one repents and is born again, he is born again with his sins forgiven. Certain denominations may teach different things, but I think the scriptural basis for such a pronouncement is at best shakey.
Killing and murder are not the same thing. All murders are killings. But not all killings are murders.