Cohesion between sister chromatids during G2 and M phases depends on the "cohesin" protein Scc1p (Mcd1p). Loss of cohesion at the metaphase to anaphase transition is accompanied by Scc1p's dissociation from chromatids, which depends on proteolysis of Pds1p mediated by a ubiquitin protein ligase called the anaphase promoting complex (APC). We show that destruction of Pds1p is the APC's sole role in triggering Scc1p's dissociation from chromatids and that Pds1p forms a stable complex with a 180 kDa protein called Esp1p, which is essential for the dissociation of Scc1p from sister chromatids and for their separation. We propose that the APC promotes sister separation not by destroying cohesins but instead by liberating the "sister-separating" Esp1 protein from its inhibitor Pds1p.