Inclusion Criteria:

- Age 22 - 50 years

- Patients will have one of the following hematological malignancies:

- Acute myelogenous leukemia (AML): Complete first remission (CR1) at high risk
for relapse or Complete second remission (CR2)

- Acute lymphoblastic leukemia (ALL): Complete first remission (CR1) at high risk
for relapse or Complete second remission (CR2)

- Acute undifferentiated leukemia (AUL) or biphenotypic leukemia: CR1 or CR2

- Myelodysplastic Syndrome (MDS) with one of the following: Low and Intermediate-1
International Prognostic Scoring System (IPSS) score with Life-threatening
neutropenia or thrombocytopenia; or Platelet transfusion dependence
Intermediate-2 or High IPSS score Therapy-related disease: patient with history
of chemotherapy and current evidence of MDS

- Patients with adequate organ function and performance status criteria

- Two Suitable Umbilical Cord Blood Units: a cryopreserved dose of at least 1.5 x 107
TNC/kg. If the unit contains red cells at time of cryopreservation, the cryopreserved
dose must be at least 2.0 x 107 TNC/kg. Each unit must be at least 4/6 HLA-A and B
antigen, and DRB1 allele matched with the recipient. Each unit must be at least 3/6
HLA-A, B DRB1 antigen matched to each other.

Exclusion Criteria:

- Patient with suitable related donor

- AML, ALL, AUL, biphenotypic leukemia beyond CR2

- AML evolved from myelofibrosis

- Any acute leukemia with:

- Morphologic relapse or persistent disease in the BM

- Active extra-medullary leukemia including active CNS leukemia

- Requiring greater than two cycles of chemotherapy to obtain present remission
status

- Bone marrow aplasia (defined as BM cellularity < 5% at transplant work-up)

- MDS with 10% or greater bone marrow blasts at pre-transplant workup

- Prior autologous or allogeneic HSC transplant at any time

- Prior radiation therapy rendering patient ineligible for TBI

- Any uncontrolled infection at time of study enrollment

- Seropositive or NAT positive for HIV or HTLV1

- Females who are pregnant or breast feeding

- Patient unable to give informed consent or unable to comply with the treatment
protocol including appropriate supportive care, follow-up, and research tests