In this paper the Clarke-Gawthrop type of self-tuning controller is modified and shown to be robust stable with respect to unmodelled plant uncertainties and bounded disturbances. A self-tuning controller is proposed here consisting of two steps: the first, an optimal control law, is derived by means of minimizing a quadratic cost function of the Clarke-Gawthrop type; the second, the optimal control law, is modified by introducing an estimate of the modelling error as a feedback. For the parameter estimation, a modified least-squares scheme with a relative dead zone is employed. The robustness results are derived by neither requiring too much a priori knowledge of the plant parameters, nor using any assumptions about the adaptive signals.