In this paper, the relationship between k consecutive outputs of the conventional differential detector and output of differential detector with k-bit delayer MSK and GMSK signal, using a k-bit delay circuit, is the product of k successive output of the conventional differential detector. This relationships are used to generalize the structure of receiver which was proposed by Makrakis using 2-bit delay line. The error rate performance of the proposed method is carried out by computer simulation and significant performance improvement is achieved for differential MSK and GMSK system.