Abstract: Based on SW theory, this paper studies the general blind deconvolution problems of non-minimum systems. A new concept of normalized cumulant stemmed from second and fourth order cumulants is defined. The normalized cumulant character of signal passing linear systems is analyzed. Then a new blind deconvolution criteria of normalized cumulant matching is presented, and a new algorithm is also derived. The usable computer simulation results for demonstration of the performance of the proposed algorithm are obtained.