This paper presents an override controller which ensures that constrained output variables retain certain prescribed strict bounds. The class of nominal closed loop systems considered is strictly proper and minimum phase, assuming the first Markov parameter to be full rank and for each output measurement constraint there is one available actuator. The advantage of the considered class of nominal systems is that an output constraint translates directly into a state constraint for which it is possible to use a particular non-smooth Lyapunov function. The non-smooth Lyapunov function is defined by the level of the output constraint creating an invariant set for which the strict output constraints are satisfied. The override strategy is designed to have only a minimal effect on the nominal control loop when no constraint is violated.