From Corollary 3.5 in [Berkani, M; Sarih, M.; Studia Math. 148 (2001), 251– 257] we know that if S, T are commuting B-Fredholm operators acting on a Banach space X, then ST is a B-Fredholm operator. In this note we show that in general we do not have ind(ST) = ind(S) + ind(T), contrarily to what has been announced in Theorem 3.2 in [Berkani, M; Proc. Amer. Math. Soc. 130 (2002), 1717–1723]. However, if there exist U, V ∈ L(X) such that S, T, U, V are commuting and US + V T = I, then ind(ST) = ind(S) + ind(T), where ind stands for the index of a B-Fredholm operator.