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SARS-CoV-2 has adapted in a stepwise manner, with multiple beneficial mutations accumulating in a rapid succession at origins of VOCs, and the reasons for this are unclear. Here, we searched for coordinated evolution of amino acid sites in the spike protein of SARS-CoV-2. Specifically, we searched for concordantly evolving site pairs (CSPs) for which changes at one site were rapidly followed by changes at the other site in the same lineage. We detected 46 sites which formed 45 CSP. Sites in CSP were closer to each other in the protein structure than random pairs, indicating that concordant evolution has a functional basis. Notably, site pairs carrying lineage defining mutations of the four VOCs that circulated before May 2021 are enriched in CSPs. For the Alpha VOC, the enrichment is detected even if Alpha sequences are removed from analysis, indicating that VOC origin could have been facilitated by positive epistasis. Additionally, we detected nine discordantly evolving pairs of sites where mutations at one site unexpectedly rarely occurred on the background of a specific allele at another site, for example on the background of wild-type D at site 614 (four pairs) or derived Y at site 501 (three pairs). Our findings hint that positive epistasis between accumulating mutations could have delayed the assembly of advantageous combinations of mutations comprising at least some of the VOCs.