The Jade Raksha(1968)

A fearsome swordswoman known as The Jade Raksha appears in the martial arts world and begins killing people whose surname is Yan. A swordsman figures out who she is, and asks her why - the answer being that a Yan killed her family 18 years ago... but she's not sure exactly which Yan it was. He suggests that killing the innocent is wrong, but she only has vengeance on her mind and is not to be convinced.