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Selenocysteine (Sec), the 21stamino acid specified by the genetic code, is a rare selenium-containing residue found in the catalytic site of selenoprotein oxidoreductases. Sec is analogous to the common cysteine (Cys) amino acid but its selenium atom offers physicalchemical properties not provided by the corresponding sulfur atom in Cys. Catalytic sites with Sec in selenoproteins of vertebrates are under strong purifying selection but one enzyme, Glutathione Peroxidase 6 (GPX6), independently exchanged Sec for Cys less than one hundred million years ago in several mammalian lineages. We reconstructed and assayed these ancient enzymes before and after Sec was lost and up to today, and found them to have lost their classic ability to reduce hydroperoxides using glutathione (GSH). This loss of function, however, was accompanied by bursts of amino acid changes in the catalytic domain, with protein sites concertedly changing under positive selection across distant lineages abandoning Sec in GPX6. This demonstrates that when sulfur in Cys impairs catalysis a narrow evolutionary path is followed, with epistasis and pleiotropy leading to convergent evolution and triggering enzymatic properties likely beyond those in classic GPXs. These findings are an unusual example of adaptive convergence towards unexplored oxidoreductase functions during mammalian evolution.