YA - two sisters discover their piano teacher was a collaborator in WWII

I read this one roughly 30 years ago.

Two sisters take lessons from a piano teacher and one suddenly becomes hostile for no apparent reason. The other sister (the protagonist) eventually learns that her sister found a picture in a library book of the piano teacher after the war and identified as a collaborator. (Possibly in France.) The teacher had fallen in love with a German soldier and was found out.