The aim of the present paper was to increase the efficiency of self-tuning minimum variance (MV) control of linear systems followed by the so-called hard nonlinearities. To this end, an approach based on reordering of observations to be processed for the reconstruction of an unmeasurable internal intermediate signal, which acts between a linear dynamic time-invariant (LTI) system and a static nonlinear block of the closed loop Wiener system with a saturation nonlinearity in an output, has been developed. The technique based on the ordinary least squares and on data partition is used for the internal signal extraction. The results of numerical simulation, identification, and self-tuning MV control as well as generalized MV control of the second-order discrete-time closed loop LTI system with the saturation nonlinearity are given by the computer. Copyright © 2012 John Wiley & Sons, Ltd.