Inclusion Criteria:

- Age 4 - 50 years

- Patient should not have a related or unrelated volunteer donor that is suitably HLA
matched and available in the required time period or be a suitable candidate for an
autologous stem cell transplant.

- Patients will have one of the following hematological malignancies: Acute myelogenous
leukemia (AML):

- Complete first remission (CR1) at high risk for relapse as defined by:

known prior diagnosis of myelodysplasia (MDS); or therapy related AML; or White cell count
at presentation > 100,000; or Presence of extramedullary leukemia at diagnosis; or
Unfavorable FAB type (M0, M5-7); or High-risk cytogenetics (such as those associated with
MDS, abnormalities of 5, 7, 8, Philadelphia chromosome, complex karyotype); or High risk
molecular markers such as FLT3 mutations; or Requirement for 2 or more inductions to
achieve CR1

- Complete second CR (CR2).

• Acute lymphoblastic leukemia (ALL):

- Complete first remission (CR1) at high risk for relapse as defined by:

White cell count at presentation as follows:

- > 100,000 if < 18 years

- > 50,000 if > 18 years; or

Presence of extensive extra-medullary disease (excluding CNS disease); or Presence of
high-risk cytogenetic abnormality such as t(9;22), t(1;19), t(4;11) or other MLL
rearrangements (11q23), t(8;14) [excluding B-ALL in pediatric patients]; or

Failed to achieve complete remission after four weeks of induction therapy Unable to
receive required consolidation chemotherapy as would be needed to maintain remission

- Complete second or third remission (CR2 or CR3)

- Acute undifferentiated leukemia (AUL), infant leukemia, or biphenotypic leukemia
in CR1, CR2 or CR3. Patients with infant leukemia must be eligible to receive
total body irradiation.

- Juvenile Myelomonocytic leukemia (JMML) with < 30% bone marrow blasts.

- Chronic myelogenous leukemia (CML)

- GleevecTM failure in 1st or 2nd chronic phase;

- Gleevec failure in 1st or 2nd accelerated phase.

• Myelodysplastic Syndrome (MDS) with one of the following:

- Low (Score 0) International Prognostic Scoring System (IPSS) score with
Life-threatening cytopenia(s); or Red cell or platelet transfusion dependent

- Intermediate (Score 1) or High (Score 2) International Prognostic Scoring System
(IPSS) score.

- Patients with bone marrow blasts > 10% should have AML induction therapy with disease
response to < 5% blasts and at least partial count recovery.

• Non-Hodgkin's Lymphoma

- Patients with high-grade disease following initial therapy and are not appropriate
for further chemotherapy or autologous stem cell transplantation.

- Patients with high-grade or diffuse large cell NHL with recurrent disease after first
remission and must have:

Chemo-sensitivity as evidenced by > partial remission (PR) (defined as > 50% reduction in
mass size after therapy).

- Patients with adequate organ function and performance status criteria as measured by:

- Karnofsky score > or = to 70 % or Lansky score > or = to 70%

- Renal: Calculated creatinine clearance > or = to 60 ml/min

- Hepatic: Total bilirubin < 2.5 mg/dL unless benign congenital hyperbilirubinemia
(Gilbert's syndrome) and ALT/AST < 3 x upper limit of normal

- Albumin > or = to 2.5

- Pulmonary: Pulmonary function (spirometry and corrected DLCO) > or = to 60% normal if
available (in small children use History and Physical and CT scan as necessary to
determine pulmonary status)

- Cardiac: Left ventricular ejection fraction > or = to 50%

- Double Unit Umbilical Cord Blood Grafts:

Units will be selected based on the HLA match to the patient and on the basis of the
individual and combined cell doses of the units.

- Patient has a related or unrelated volunteer donor that is suitably HLA matched and
available in the required time period.

- Patient is a candidate for an autologous stem cell transplant.

- Active CNS leukemia.

- Acute Myelogenous Leukemia in greater than CR2.

- Acute Myelogenous Leukemia evolved from myelofibrosis.

- Acute Lymphoblastic Leukemia, acute undifferentiated leukemia, biphenotypic leukemia
or infant leukemia greater than CR3.

- Any acute leukemia with:

- Morphologic relapse or persistent disease in the BM (cytogenetic relapse without
morphologic evidence of relapse or cytogenetic persistent disease in the BM is
acceptable); or

- Active extra-medullary leukemia; or

- Requiring greater than 2 cycles of chemotherapy to obtain present remission
status;

- Bone Marrow aplasia (defined as BM cellularity less than 5% at transplant work-up);
or

- MDS with greater than 10% bone marrow blasts refractory to chemotherapy; or

- CML in blast crisis; or

- NHL refractory to chemotherapy (less than PR after 2 or more regimens); or

- Prior autologous or allogeneic HSC transplant at any time; or

- Prior radiation therapy rendering patient ineligible for TBI; or

- Uncontrolled viral, bacteria or fungal infection at time of study enrollment; or

- Seropositive or NAT positive for HIV; or

- Females who are pregnant or breast feeding; or

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