The paper presents a differential detection scheme for noncoherent detection of digital FM signals received over bandwidth restricted channels. The new differential detection scheme observes the phase of the FM signal at centres of signalling intervals to derive the differential phase. Differential encoding of transmitted data is required for preventing error propagation. Numerical results show that the new differential detector yields a superior performance in narrowband channels where conventional differential detection becomes unusable. Error probabilities and optimum BT values are presented assuming that bandlimiting is caused solely by IF filtering.