A method of suppressing rejection of transplanted organ tissue comprising the step of administering to an organ transplant patient, either before, during, or after transplantation, a pharmaceutical composition that comprises an antibody and a physiologically acceptable carrier wherein the antibody is comprised of a heavy chain having a variable region with a sequence as shown in SEQ ID NO:13 or SEQ ID NO:14 and a human IgG4 constant region, and a light chain having a variable region with a sequence as shown in SEQ ID NO:9 or SEQ ID NO:18, wherein the human IgG4 constant region comprises a point mutation from leucine to glutamic acid at residue 235.