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SummarySuccessful segregation of chromosomes during mitosis and meiosis depends on the action of the ring-shaped condensin complex, but how condensin ensures the complete disjunction of sister chromatids is unknown. We show that the failure to segregate chromosome arms, which results from condensin release from chromosomes by proteolytic cleavage of its ring structure, leads to a DNA damage checkpoint-dependent cell-cycle arrest. Checkpoint activation is triggered by the formation of chromosome breaks during cytokinesis, which proceeds with normal timing despite the presence of lagging chromosome arms. Remarkably, enforcing condensin ring reclosure by chemically induced dimerization just before entry into anaphase is sufficient to restore chromosome arm segregation. We suggest that topological entrapment of chromosome arms by condensin rings ensures their clearance from the cleavage plane and thereby avoids their breakage during cytokinesis.