LetJbe a holomorphic mapping whereis a domain with real analytic boundary ∂Ω such that. SupposeJmaps ∂Ω into an algebraically normal real hypersurface ∑ By closely following the argument of Boauendi and Rotschild |2. 4| we prove the following results. Theorem 1: Ifis rigid andJis nondegenerate at point. thenJextends holomorphically to a full neighbourhood of ρ. Theorem 2: If ∂Ω and ∑ are of infinite type andJnot completely degenerate, thenJextends holomorphically to a full neighborhood of ρ