The guarantee of feasibility given feasibility at initial time is an issue that has been overlooked by many of the recent papers on stochastic model predictive control. Effective solutions have recently been proposed, but these carry considerable online computational load and a degree of conservativism. For the case that the elements of the random additive disturbance vector are independent, the current paper ensures that probabilistic constraints are met and that a quadratic stability condition is satisfied. A numerical example illustrates the efficacy of the proposed algorithm, which achieves tight satisfaction of constraints and thereby attains near-optimal performance. (C) 2010 Elsevier Ltd. All rights reserved.