Patients receive high-dose chemotherapy and/or radiotherapy as a conditioning regimen beginning 6-9 days before the umbilical cord blood transplant (UCBT). The regimen varies according to the underlying cause of the anemia, but could include busulfan, cyclophosphamide or melphalan, anti-thymocyte globulin or methylprednisolone, and/or radiation therapy. One day after the conditioning regimen is completed, patients receive the UCBT.