A method for inhibiting rejection of tissues transplanted into a mammalian host is disclosed. Treatment of the tissues with an enzyme or combination of enzyme, particularly papain, to eliminate cell surface structures necessary for recognition by the host's immune system, particularly MHC Class I molecules, avoids or reduces the attack of the host's immune system on the transplanted tissues. Tissues that are enzymatically shaved of MHC Class I antigens and/or other critical adhesion molecules can be rendered at least temporarily resistant or immune to attack by cytolytic T lymphocytes, helper T lymphocytes, antibodies, or other effector cells of a host's immune system, thereby enhancing the survivability of the tissues in the host after transplant.