Born to Kill - Robert Wise

In Reno a man kills a girl he likes and her boyfriend out of jealousy; it may not be the first time. A woman whose divorce has just come through finds the bodies but decides not to become involved. The two meet next day on the train to San Francisco unaware of this link between them. They are attracted to each other, and the relationship survives his marriage to her half-sister for money and status. It even survives the woman discovering that he was the murderer, though she may not realise how easily someone who has killed this way before can do so again.