This technical note presents an improved version of the Feed-Forward Command Governor (FF-CG) strategy recently proposed in [1] for the supervision of input/state constrained discrete-time linear systems subject to bounded disturbances, whose main feature is not to require any explicit on-line measure (or estimation) of the state for its implementation. Although effective also in the case of bounded disturbances, the performance of earlier FF-CG schemes [1] was mainly limited by the fact that such strategies were required to maintain constant their actions for a prescribed number of sampling steps. Here such a restriction is removed and the proposed FF-CG solution is allowed to update its action at each sampling step. Numerical simulations on a physical plant have been undertaken and comparisons with other strategies have been reported in order to show the effectiveness of the proposed approach.