About fifty years ago, N.A.Morozov found three pairs of ruling ancient dynasties for which the sequences of lengths (periods) of reign, represented visually on the time line, bore a striking resemblance to one another. He suggested that in each case the two dynasties are actually reflections of a single real dynasty which "became multiplied" as a result of a mistaken dating of the different texts describing the same events. But it is not enough to rely upon subjective impression. For this reason we set about creating a formal quantitative method for determining whether two dynasties are merely different manifestation of a single dynasty ("dependent dynasties") or are truly distinct ("independent dynasties"). The application of the method to historical data traditionally believed to belong to earlier than the 13th c.A.D. unexpectedly led to the discovery of pairs of dynasties regarded as independent in all the senses, but for which the special proximity coefficient is extremely small.