Abstract: The invention provides a method to prevent or ameliorate hyperacute or acute rejection of a human donor organ transplanted to a human recipient. Hyperacute rejection would normally occur after a human subject receives a transplanted human organ against which the subject has preformed anti-HLA antibodies. Acute rejection occurs when the recipient of a human organ forms antibodies against that organ after transplant. The invention method comprises passing the plasma of the recipient over a sterile and pyrogen-free column coupled to anti-human immunoglobulin antibodies which bind to and remove a significant portion of the immunoglobulin from the subject's plasma.