In this paper, we introduce a new notion of strong pseudo-amenability for Banach alge16 bras. We study strong pseudo-amenability of some matrix algebras. Using this tool, we characterize strong pseudo-amenability of 1 17 (S), provided that S is a uniformly 18 locally finite inverse semigroup. As an application, we show that for a Brandt semigroup S = M0(G, I), 1 19 (S) is strong pseudo-amenable if and only if G is amenable and I is 20 finite. We give some examples to show the differences between strong pseudo-amenability 21 and the other classical notions of amenability.
