The control of a class of multivariable systems described by linear vector difference equations with constant but unknown parameters is discussed. A strategy using a generalized cost-function is first presented. A multivariable self-tuning regulator based on this generalized minimum variance strategy is then proposed. It uses a recursive multiple least squares estimator and a linear matrix controller obtained directly from the estimates. The algorithm can be considered as a multivariable generalization of Clarke's self-tuning controller.