Search the name of an old movie or TV show episode (crime thriller) from 1950s or 1960s

Hi,
I am searching for the name of an old movie or an episode of a TV series from 1950s or 1960s. It could be a Alfred Hitchcock work, but I can not find any movie description that matchs the plot I know. It was definitely a film in black white.
The plot is something like: After a serie of murders of women, a young man was suspected and arrested. But then another murder happend. Eventually the detective could find out that the murderer’s girlfriend or his wife or his sister (I don’t exsactly know.) committed the last murder to provide him an alibi, because all of his victims were elderly, but the new one was a younger woman.