Getsurin ni Kiri Saku

From MangaHelpers:

A new transfer student has come into town, a girl with a mysterious air and black clothing who is called Inugami Sakuya. What few know is that by moonlight, she hunts and kills those possessed by "Inugami." A man can become possessed by being bitten, leading to a nighttime transformation into a beast driven to eat women. Sakuya gets no thanks for brutally ending the lives of these unfortunate men with her sword, and she is often too late to save the women they threaten. Sakuya also must deal with her own inner demons, which are all too real.