In this paper, we are concerned with the problems of fault- detection for combinational logic networks. The method which we can obtain the complete test sets using propagation of primitive test sets is presented by considering the relation between test sets of each line. A new method is proposed that can detect the fault through the observation of the output variance by applying only the test sets equivalent to the number of inputs We found that the method is much improved compared to the conventional fault detecting procedure that requires applying the complete test sets to the logic networks.