This paper presents multivariable self-tuning controllers (STC) based on a generalized minimum variance strategy, that is reference signals and weighting of the real control effort are taken into account in the cost function. An extension of the STC's of Schumann [23], Favier [8]-[9], Koivo [19], and Keviczky and Kumar [17] is obtained by minimizing a more general cost function and by considering the case of MIMO systems having a number of inputs and outputs which can be mutually different. Several controllers are derived as particular cases of the controller developed in this paper. Simulation results illustrate advantages of the obtained STC compared with those quoted above.