In this paper, we introduce a notion of ultra central approximate identity for Banach algebras which is a generalization of the bounded approximate identity and the central approximate identity. Using this concept we study pseudo-contractibility of some matrix algebras among ℓ1-Munn algebras. As an application, for the Brandt semigroup S = M 0(G, I) over a non-empty set I, we show that ℓ1(S) has an ultra central approximate identity if and only if I is finite. Also we show that the notion of pseudo-contractibility and contractibility are the same on ℓ1(S)∗∗, where S is the Brandt semigroup.
