Abstract. In this paper we study the relation between module amenability of θ -Lau product A× θ B and that of Banach algebras A, B. We also discuss module biprojectivity of A× θ B. As a consequent we will see that for an inverse semigroup S, l 1 (S) × θ l 1 (S) is module amenable if and only if S is amenable
