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Proteins with two similar motifs in tandem are one of the most common cases of tandem repeat proteins. The question arises: why is the first emerged repeat frequently fixed in the process of evolution, despite the ample opportunities to continue its multiplication at the DNA level? To answer this question, we systematically analyzed the structure and function of these proteins. Our analysis showed that, in the vast majority of cases, the structural repetitive units have a two-fold (C2) internal symmetry. These closed structures provide an internal structural limitation for the subsequent growth of the repeat number. Frequently, the units "swap" their secondary structure elements with each other. Moreover, the duplicated domains, in contrast to other tandem repeat proteins, form binding sites for small molecules around the axis of C2 symmetry. Thus, the closure of the C2 structures and the emergence of new functional sites around the axis of C2 symmetry provide plausible explanations for why a repeat, once appeared, becomes fixed in the evolutionary process. We have placed these structures within the general structural classification of tandem repeat proteins, classifying them as either Class IV or V depending on the size of the repetitive unit., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2023 Elsevier Inc. All rights reserved.)