Abstract: The narrowing relation over terms constitutes the basis of the most important operational semantics of languages that integrate functional and logic programming paradigms. It also plays an important role in the definition of some algorithms of unification modulo equational theories which are defined by confluent term rewriting systems. Due to the inefficiency of simple narrowing, many refined narrowing strategies have been proposed in the last decade. This paper presents a new narrowing strategy which is optimal in several respects. For this purpose we propose a notion of a needed narrowing step that, for inductively sequential rewrite systems, extends the Huet and L