No / An algorithm called VPAStab is given for the acceleration of convergence of a sequence of vectors. It combines a method of vector-Padé approximation with a successful technique for stabilisation. More generally, this algorithm is designed to find the fixed point of the generating function of the given sequence of vectors, analogously to the way in which ordinary Padé approximants can accelerate the convergence of a given scalar sequence. VPAStab is justified in the context of its application to the solution of a large sparse system of linear equations. The possible breakdowns of the algorithm are listed. Numerical experiments indicate that these breakdowns can be classified either as pivot-type (type L) or as ghost-type (type D).