In this paper, the output of a differentially coherent detector using the phase of thekth previous bit as a reference is derived under noise free conditions for binary differential phase shift keyed signals, wherek = 1, 2, 3 ...or ally integer. This is then related to the output of a conventional differentially coherent detector (k = 1). In the presence of noise, this output relationship changes depending on which detector has made an error in detection. This property can be used to reduce the error rate for differentially coherent systems. A receiver consisting of a first-order (conventional) and second-order detectors, where the references are the phase of the previous and second previous bits, respectively, is analyzed theoretically. The result shows that the amount of improvement in error rate due to the addition of the second-order detector depends on the percentage of single errors in the conventional detector. If the error rate of a conventional differentially coherent system is close to the optimum, the theoretical improvement using the additional detector is small (≃ 0.2 dB). However, it is shown experimentally that if the original performance is poor due to intersymbol interference, then considerable improvement is possible with an additional detector (≃ 1.6 dB). In addition to error rate improvement, the circuit also provides error rate information that can be used for in-service performance monitoring and as a sensor for automatic equalizers.