The design of linearizing compensators via output-feedback for discrete-time non-linear plants, using I/O measurements only, is typically performed in an indirect way by identifying first a non-linear model of the plant, and resorting then to a suitable model-based design technique. In this paper we propose the use of a new method, based on a virtual input direct design (VID2) approach. The main feature of such a method is to carry the control design into a standard non-linear mapping approximation problem, thus avoiding any preliminary plant-identification phase. As compared with the existing methods, the new one requires less computational effort, while taking full advantage of the non-linear approximation software tools already available. In this paper, the new method is described, and some theoretical results are given, concerning the I/O linearization of discrete-time systems via dynamic output feedback.