The author finds a finite pseudoidentity basis for the semigroup pseudovariety generated by all finite 0-simple semigroups. The basis consists of the following four pseudoidentities: (1) \((xy)^{\omega+1}x=xyx\); (2) \(x^{\omega+2}=x^2\); (3) \((xyz)^\omega xhz=xhz(xyz)^\omega\); (4) \((xy)^\omega xzx=xz(xy)^\omega x\). This implies that the pseudovariety in question has decidable membership. Reviewer's remarks: 1. It can be shown that each of the pseudoidentities (3) and (4) implies the other modulo (1) and (2). The basis found in the paper can therefore be reduced to (1), (2), (3) or (1), (2), (4). 2. The results in the paper have been independently obtained by \textit{T. E. Hall, S. I. Kublanovskij, S. Margolis, M. V. Sapir} and \textit{P. G. Trotter} [Decidable and undecidable problems related to completely 0-simple semigroups. J. Pure Appl. Algebra (to appear)].