In this paper, we present a novel test pattern generator for pseudoexhaustive testing. This generator bridges the gap between convolved LFSR/SR and permuted LFSR/SR. It is considered to be the optimal pseudoexhaustive test pattern generator as far as the lengths of test set and hardware overhead are concerning. We present an efficient search to assign the residues for the inputs of the CUT to increase the chance to get several solutions and reduce the hardware overhead. With small number of permutations in the assigned residues, the chance of obtaining efficient results may be increased. The novel generator is considered the general form of the pseudoexhaustive test pattern generator. The simple LFSR/ SR, the permuted LFSR/SR, and convolved LFSR/SR are considered the special case of the novel generator. The experimental results indicate the superiority of this generator and the efficiency of our approach.