The centromere is important for segregation of chromosomes during cell division in eukaryotes. Its destabilization results in chromosomal missegregation, aneuploidy, hallmarks of cancers and birth defects. In primate genomes centromeres contain tandem repeats of ~171 bp alpha satellite DNA, commonly organized into higher order repeats (HORs). In spite of crucial importance, satellites have been understudied because of gaps in sequencing - genomic “black holes”. Bioinformatical studies of genomic sequences open possibilities to revolutionize understanding of repetitive DNA datasets. Here, using robust (Global Repeat Map) algorithm we identified in hg38 sequence of human chromosome 21 complete ensemble of alpha satellite HORs with six long repeat units (≥20 mers), five of them novel. Novel 33mer HOR has the longest HOR unit identified so far among all somatic chromosomes and novel 23mer reverse HOR is distant far from the centromere. Also, we discovered that for hg38 assembly the 33mer sequences in chromosomes 21, 13, 14, and 22 are 100% identical but nearby gaps are present; that seems to require an additional more precise sequencing. Chromosome 21 is of significant interest for deciphering the molecular base of Down syndrome and of aneuploidies in general. Since the chromosome identifier probes are largely based on the detection of higher order alpha satellite repeats, distinctions between alpha satellite HORs in chromosomes 21 and 13 here identified might lead to a unique chromosome 21 probe in molecular cytogenetics, which would find utility in diagnostics. It is expected that its complete sequence analysis will have profound implications for understanding pathogenesis of diseases and development of new therapeutic approaches.