Muramasa

Shiro Masakatsu is a boy people can't stand to touch, whether they are male or female. One day, he sees a girl with a weird katana finishing a fight with someone, so naturally, he ran away. He later meets the same girl at school, and another katana-wielder picking a fight with her. But it turns out these katanas have abilities, called Youtou, making them cursed katanas; but to use their Youtou, a certain condition has to be met...
(Source: MangaHelpers)