The hypothesis of the study is double unit umbilical cord blood transplantation in adults will be associated with a one year survival rate of at least 40%.

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