This note presents a new approach to guaranteeing stability of model predictive control (MPC). A stability constraint is computed and propagated forward at each stage as a constraint on the magnitude of the predicted state vector for a state-space controllable-form realization. It is shown that asymptotic stability is guaranteed for the case of constrained multi-input linear time-invariant systems under full-state measurement or with state estimation for any prediction horizon and any optimization objective function.