Some approaches in logical network synthesis use decomposition of a switching function into partial ones, which possess properties convenient for an optimal realization. The total complex decomposition (TCD) is one of such methods introduced in previous papers. It appeared to be very useful in the realization employing some logic strictures known as programmable logic arrays. The method of using TCD in order to find a representation of switching function suitable for realization with chosen architecture has been already proposed. As a continuation of this method, the paper presents matrixes relations for examination of TCD with specific properties. Classes of matrixes convenient for using fast algorithms of FTF type have been worked out. The proposed procedure examines noted type of decomposition and, in the case of its existence, finds composite expr essions needed for direct realization.