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The ability to predict emerging variants of SARS-CoV-2 would be of enormous value, as it would enable proactive design of vaccines in advance of such emergence. Based on molecular evolutionary analysis of S protein, we found a significant correspondence in the location of amino acid substitutions between SARS-CoV-2 variants recently emerging and their relatives that infected bat and pangolin before the pandemic. This observation suggests that a limited number of sites in this protein are repeatedly substituted in independent lineages of this group of viruses. It follows, therefore, that the sites of future emerging mutations in SARS-CoV-2 can be predicted by analyzing their relatives (outgroups) that have infected non-human hosts. We discuss a possible evolutionary mechanism behind these substitutions and provide a list of frequently substituted sites that potentially include future emerging variants in SARS-CoV-2.