The binding of 2,578 human miRNAs with the mRNAs of 12,175 human genes was studied. It was established that miR-619-5p, miR-5095, miR-5096, and miR-5585-3p bind with high affinity to the mRNAs of the 1215, 832, 725, and 655 genes, respectively. These unique miRNAs have binding sites in the coding sequences and untranslated regions of mRNAs. The mRNAs of many genes have multiple miR-619-5p, miR-5095, miR-5096, and miR-5585-3p binding sites. Groups of mRNAs in which the ordering of the miR-619-5p, miR-5095, miR-5096, and miR-5585-3p binding sites differ were established. The possible functional and evolutional properties of unique miRNAs are discussed.