Antiphospholipid syndrome is disease believed to be due to immune cells, cells which normally protect the body, but are now producing the protein which leads to abnormal clotting in the body. This study is designed to examine whether treating patients with high dose cyclophosphamide together with CAMPATH (drugs which reduce the function of the immune system), followed by return of the previously collected stem cells will result in improvement in the disease. Stem cells are undeveloped cells that have the capacity to grow into mature blood cells, which normally circulate in the blood stream. The purpose of the intense chemotherapy is to destroy the cells in the immune system which may be causing the disease. The purpose of the stem cell infusion is to produce a normal immune system that will no longer attack the body. The study purpose is to examine whether this treatment will result in improvement in the disease. The drugs used in this study treatment are drugs for commonly used for immune suppression.