Abstract: There have been a great many of studies on the pointed representations of finite-dimensional sanple Lie algebras.cf.[1][2]etc.In this paper we give a new proof of animpottant Lemma,and from this we derive our main result:Irreducible pointed modules of finite-dimesional simple Lie algebras are all Harish-Chandra modules.

Key words:  , Lie algebra, algebra homomorphism