The Supreme Court has denied Mikael Penttilä leave to appeal the life sentence he received for his conviction of a 2018 murder.
The life sentence remains in force for the killing, in which Penttilä strangled his victim in her flat.
The appeals court ruled that the violence used in the murder was cruel and served as an aggravating factor in the sentencing.
Penttilä was adjudged to have caused great suffering and tortured his victim. He claimed he had not deliberately tortured his victim and the life sentence should be reduced.
He also claimed he had not intended to kill the women when he went to her apartment, but the situation got out of hand when she recognised him.
He has previously been convicted of strangling to death his own mother, a 12-year-old girl and a third woman, and was sentenced to prison terms of varying duration for each crime.
He was also convicted of planning a violent crime, in which the intended victim was a 17-year-old girl.