In this work it is shown in detail the necessary steps to compute the erros probability taking into account the intersymbol interference due to the frequency-selective fading in the communication channel. A comparison is made between Bello and Nelin’s and Bailey and Lindenlaub’s results for the error probabilities with intersymbol interference due to two adjacent pulses with the sample pulse. It is concludes that the work done by the latter can be considered correct and the assumed approximations are discussed. There is developed a means of computation which permits obtaining without approximation the error probabilities with intersymbol interference due to four and two adjacent pulses to the sampled pulse: It is necessary to remark that this work was done for a digital communication system with differentially coherent matched filter receivers. The binary pulse sequence was transmitted through a channel with pure frequency selective fading described by its Gaussian frequency autocorrelation function.