Tanith Lee 
Black Unicorn 

Nobody knew where it had come from, or what it wanted. Not even Jaive, the sorceress, could fathom the mystery of the fabled beast. But Tanaquil, Jaive’s completely unmagical daughter, understood it at once. She knew why the unicorn was there: It had come for her. It needed her. Tanaquil was amazed because she was the girl with no talent for magic. She could only fiddle with broken bits of machinery and make them work again. What could she do for a unicorn?