Inclusion Criteria:

- Disease Status: NHL, HD, or MM refractory to chemotherapy or relapsed; CLL Rai Stage
III/IV, or lymphocyte doubling time of 6 months, or Stage I/II resistant to 2
chemotherapy regimens; AML or ALL in second or subsequent remission or in first
remission with adverse cytogenetics or antecedent hematologic disorder

- Estimated disease-free survival of less than one year

- ECOG performance status of 0, 1, 2

- Lack of 6/6 or 5/6 HLA matched related or 6/6 matched unrelated donor, or a donor is
not available within the time frame necessary to perform a potentially curative stem
cell transplant

- 4/6 or greater HLA A, B, CRB1 cord blood units with a combined nucleated cell dose
from of > 3.7 x 10(7) NC/kg

Exclusion Criteria:

- Cardiac disease: symptomatic congestive hearth failure or RVG or echocardiogram
determined left ventricular ejection fraction of < 45%, active angina pectoris, or
uncontrolled hypertension

- Pulmonary Disease: severe chronic obstructive lung disease, or symptomatic
restrictive lung disease, or corrected DLCO of < 50%

- Renal disease: serum creatinine > 2.0 mg/dl

- Hepatic disease: serum bilirubin > 2.0 mg/dl (except in the case of Gilbert's
syndrome), SGPT or SGOT > 3 x normal

- Neurologic disease: symptomatic leukoencephalopathy, active DNS malignancy or other
neuropsychiatric abnormalities believed to preclude transplantation

- HIV antibody or Hepatitis B surface antigen positivity

- Uncontrolled infection

- Pregnancy or breast-feeding mother