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Previous work (Kouvaritakis et al., 1992) proposed the introduction of a Youla parameter into the receding horizon control strategy to enhance the degree of robustness of the closed loop system without affecting the optimality of nominal performance. The idea is clearly appealing and has been investigated further by a number of researchers. Yet to date the application of the idea has only been considered for the case of unconstrained systems, which is surprising given that the presence of constraints is main justification for the use of MPC for linear systems. It is the purpose of the present paper to combine recent results on invariance, feasibility and an augmented and autonomous formulation of the predicted dynamics to derive an effective robust constrained MPC algorithm that takes full advantage of the introduction of a suitable Youla parameter. The efficacy of the proposed algorithm is illustrated by means of a numerical example.