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Here we present three interesting novel human Higher-Order Repeats (HORs) discovered using the HOR-searching method with GRM algorithm: (a) The novel Neuroblastoma Breakpoint Family gene (NBPF) 3mer HOR, discovered applying GRM algorithm to human chromosome 1 (Paar et al., Mol Biol Evol 28:1877-1892, 2011). NBPF 3mer HOR is based on previously known ~1.6 kb NBPF primary repeat monomers (known as DUF1220 domain) in human chromosome 1, but the NBPF HOR was not known before its discovery by using GRM. It should be stressed that the NBPF HOR presents a unique human-specific pattern, distinguishing human from nonhuman primates. (b) The novel quartic HOR (2mer⊃2mer⊃9mer) discovered using the GRM algorithm for analysis of hornerin genes in human chromosome 1 (Paar et al., Mol Biol Evol 28:1877-1892, 2011). This quartic HOR is based on 39 bp hornerin primary repeat monomer in human chromosome 1. To our knowledge, this is the first known case of quartic HOR, with four levels of hierarchy of HOR organization. (c) The novel 33mer alpha satellite HOR in human chromosome 21, discovered using the GRM algorithm (Glunčić et al., Sci Rep 9:12629, 2019). This 33mer HOR in the smallest human chromosome is the largest alpha satellite HOR copy among all 22 somatic human chromosomes. Moreover, the same 33mer HOR is present in the hg38 human genome assembly of four human chromosomes: 21, 22, 13, and 14. We point out that the DUF1220 encoding genomic structures in NBPF genes in human chromosome 1, recently studied and related to the brain evolution and pathologies and cognitive aptitude, can be considered in the framework of the general concept of HORs, already extensively studied in genomics, especially in the centromeric region., (© 2021. The Author(s), under exclusive license to Springer Nature Switzerland AG.)