In a previous study, we showed that centromere repositioning, that is the shift along the chromosome of the centromeric function without DNA sequence rearrangement, has occurred frequently during the evolution of the genus Equus. In this work, the analysis of the chromosomal distribution of satellite tandem repeats in Equus caballus, E. asinus, E. grevyi, and E. burchelli highlighted two atypical features: 1) several centromeres, including the previously described evolutionary new centromeres (ENCs), seem to be devoid of satellite DNA, and 2) satellite repeats are often present at non-centromeric termini, probably corresponding to relics of ancestral now inactive centromeres. Immuno-FISH experiments using satellite DNA and antibodies against the kinetochore protein CENP-A demonstrated that satellite-less primary constrictions are actually endowed with centromeric function. The phylogenetic reconstruction of centromere repositioning events demonstrates that the acquisition of satellite DNA occurs after the formation of the centromere during evolution and that centromeres can function over millions of years and many generations without detectable satellite DNA. The rapidly evolving Equus species gave us the opportunity to identify different intermediate steps along the full maturation of ENCs.