One of the most important models in the literature of belief change is update, defined by Katsuno and Mendelzon in 1992. In their work, KM mentioned erasure as the counterpart change of update. However, erasure was only defined at the basic level. In this paper: (1) we complete the axiomatics of erasure and provide its relation with update via the Levi and Harper Identities, and (2) we provide a semantics in terms of possible worlds.