Do you know the title of this movie?

It's an Oriental (I guess Japanese or Korean, not sure) black&white movie I happened to watch on TV at late night. Couldn't find out the title, though. It's the story of a professional hitman. He kills people for a price. He is hired to assassinate important people, politicians and suchlike. He always works alone. All he earns, he puts away in order to fulfill his obsession: to buy the land by the sea where his mother committed suicide when he was a child and they were a very poor family. He lives in a small room by the railroad, and has no friends. Eventually he gets to know a young woman he met by chance... I will not say the ending as it might be a spoiler.