Recent advances in long-read sequencing opened a possibility to address the long-standing questions about the architecture and evolution of human centromeres. They also emphasized the need for centromere annotation (partitioning human centromeres into monomers and higher-order repeats [HORs]). Although there was a half-century-long series of semi-manual studies of centromere architecture, a rigorous centromere annotation algorithm is still lacking. Moreover, an automated centromere annotation is a prerequisite for studies of genetic diseases associated with centromeres and evolutionary studies of centromeres across multiple species. Although the monomer decomposition (transforming a centromere into a monocentromere written in the monomer alphabet) and the HOR decomposition (representing a monocentromere in the alphabet of HORs) are currently viewed as two separate problems, we show that they should be integrated into a single framework in such a way that HOR (monomer) inference affects monomer (HOR) inference. We thus developed the HORmon algorithm that integrates the monomer/HOR inference and automatically generates the human monomers/HORs that are largely consistent with the previous semi-manual inference.