This research protocol is therefore designed to evaluate the safety and effectiveness of transplantation with ex vivo expanded UCB (CordIn(TM)) to overcome the high incidence of graft rejection associated with conventional UCB for aplastic anemia, where graft rejection occurs in up to 50% of subjects. We believe, based on preliminary data, that transplantation of CordIn(TM) will not only lead to rapid engraftment, but will also lead to sustained hematopoiesis, expedited immune recovery, and will reduce the chance of cord graft failure in this setting, potentially obviating the need for co-transplanting haploidentical CD34+ cells as a stem cell back-up. This phase II study is designed to have two cohorts: cohort 1 is intended to establish (in as safe a manner as possible) preliminary pilot data to support the capacity for the CordIn unit to engraft in patients with SAA in the presence of haplo CD34+ cells. For cohort 1, three to six subjects will be conditioned then will be transplanted with the thawed CordIn(TM) unit (consisting of the cultured fraction and the non-cultured fraction of the same CBU) and approximately 3 x 106 CD34+ cells/kg from a haploidentical donor which will serve as a backup stem cell source should cord graft failure occur. If 3 of the first 3 to 4 subjects or 4 of 6 subjects achieve early and sustained engraftment (defined as ANC >500 cells/ul by day 26 and a calculated cord ANC >500 cells /ul by day 42 sustained at day 100), the study will move to cohort 2 where up to 23 subsequent subjects will be transplanted with the CordIn(TM) unit alone. For cohort 2, haplo-identical cells will still be collected and cryopreserved as a back-up stem cell source but will not be infused unless there is evidence for failing cord blood engraftment (defined as an ANC < 100 by day 18 or ANC <500 by day 26). In this scenario, the cryopreserved haploidentical donor cells will be thawed and infused to abort impending cord blood engraftment failure.