A new method of the feedback linearization procedure of MIMO systems is developed. Some control variables are sacrificed and made equal to a linear combination of new states. Subsequently the feedback linearization procedure is carried out using the remaining control variables. The formal Lemma is stated and proved. A class of non-linear systems is defined, for which the derived procedure works well. The developed procedure works on plants, which are not feedback linearizable in a standard way. An example of power plant station was examined.