Human centromeres are defined by chromatin containing the histone H3 variant CENP-A assembled onto repetitive alphoid DNA sequences. By inducing rapid, complete degradation of endogenous CENP-A, we now demonstrate that once the first steps of centromere assembly have been completed in G1/S, continued CENP-A binding is not required for maintaining kinetochore attachment to centromeres or for centromere function in the next mitosis. Degradation of CENP-A prior to kinetochore assembly is found to block deposition of CENP-C and CENP-N, but not CENP-T, thereby producing defective kinetochores and failure of chromosome segregation. Without the continuing presence of CENP-A, CENP-B binding to alphoid DNA sequences becomes essential to preserve anchoring of CENP-C and the kinetochore to each centromere. Thus, there is a reciprocal interdependency of CENP-A chromatin and the underlying repetitive centromere DNA sequences bound by CENP-B in the maintenance of human chromosome segregation.