Partitioning of the genome in meiosis occurs through two highly specialized cell divisions, named meiosis I and meiosis II. Step-wise cohesin removal is required for chromosome segregation in meiosis I, and sister chromatid segregation in meiosis II. In meiosis I, mono-oriented sister kinetochores appear as fused together when examined by high-resolution confocal microscopy, whereas they are clearly separated in meiosis II, when attachments are bipolar. It has been proposed that bipolar tension applied by the spindle is responsible for the physical separation of sister kinetochores, removal of cohesin protection, and chromatid separation in meiosis II. We show here that this is not the case, and initial separation of sister kinetochores occurs already in anaphase I independently of bipolar spindle forces applied on sister kinetochores, in mouse oocytes. This kinetochore individualization depends on separase cleavage activity. Crucially, without kinetochore individualization in meiosis I, bivalents when present in meiosis II oocytes separate into chromosomes and not sister chromatids. This shows that whether centromeric cohesin is removed or not is determined by the kinetochore structure prior to meiosis II.