There is disclosed a method of preparing a non-human tissue for xenotransplantation, comprising the steps of: (i) incubating the non-human tissue with an enzyme having ±-galactosidase activity, thereby cleaving immunodominant ±1-3 linked terminal galactose residues from the tissue, and (ii) isolating the non-human tissue from the enzyme and the enzymatically-cleaved immunodominant galactose residues, thereby rendering the non-human tissue suitable for xenotransplantation into humans.