The girl is accepted to study under a master dancer. While at his house she meets the local doctor. The house is on top of the cliff. There are stairs leading up the cliff to the house. At the end of the book, the teacher makes her dance near the stairs and she cuts her leap short to keep from falling down the stairs. She looks up to see the doctor there and realizes that he has come to save her. The dancing master was trying to kill her. I think the word stairs or steps is in the title. I first read the book in the early 1970s.