We tested whether cleavage failure as a transient event establishes an incidence of centrosome amplification in cell populations. Five rounds of ∼30% cytochalasin-induced cleavage failure in untransformed human cell cultures did not establish centrosome amplification in the short or long terms. The progeny of binucleate cells progressively dropped out of the cell cycle and expressed p53/p21, and none divided a fourth time. We also tested whether cleavage failure established centrosome amplification in transformed cell populations. Tetraploid HCT116 p53^−/− cells eventually all failed cleavage repeatedly and ceased proliferating. HeLa cells all died or arrested within four cell cycles. Chinese hamster ovary cells proliferated after cleavage failure, but five rounds of induced cleavage failure produced a modest increase in the incidence of centrosome amplification in the short term, which did not rise with more cycles of cleavage failure. This incidence dropped to close to control values in the long term despite a 2–6% rate of spontaneous cleavage failure in the progeny of tetraploid cells.