An electronic system was developed for coincidence measurements in the presence of a high level of accidental coincidences, assuming the true coincidence rate is constant. This system eliminates the distortions produced by the use of two independent coincidence modules for measuring accidental coincidencesnaand the sum of accidental and real coincidencesns. The two quantities are measured by the same coincidence module during successive periods of 40 msec. The system was tested under conditions such that the accidental coincidence counts exceeded the number of real coincidences by a factor of 102. The accuracy of the measurement of real coincidences was limited only by statistical fluctuations of accidental coincidences.