Inclusion Criteria:

- The candidate must have an incurable hematological malignancy or non-malignant
hematological disorder and be eligible for transplant by the UM program.

- The candidate must have a life expectancy of less than one year without
transplantation.

- The candidate must have two partially HLA-matched UCB (cord blood) units.Units must
be HLA-matched minimally at 4 of 6 HLA-A and B (at intermediate resolution by
molecular typing) and DRB1 (at high resolution by molecular typing) loci. Units must
be HLA-matched at 3 of 6 HLA- A, B, DRB1 loci with each other (using same resolution
of molecular typing as indicated above).

- The candidate must have access to two appropriately HLA-matched units that are
available such that one unit delivers a pre-cryopreserved nucleated cell dose of at
least 2.5 x 107 per kilogram and the second unit at least 2.0 x 107 per kilogram.

Exclusion Criteria:

- The candidate is an adult or pediatric patient who has a suitable related or
unrelated donor available for transplant. Suitable donors include 8/8 (HLA-A,B,C and
DR, with all loci high-resolution typing) or 7/8 related or unrelated donor available
within 42 days of search initiation.

- The candidate has a Karnofsky (Adult) or Lansky (Pediatrics) performance status of <
70% at the time of admission for HSCT.

- The candidate is a patient with evidence of HIV infection.

- The candidate is a patient with active bacterial, fungal or viral infection not
responding to treatment. Non-response to treatment is determined by body
temperature, blood culture results, and radiographic findings as applicable.

- The candidate is pregnant.

- The candidate has any medical comorbidities/conditions that, in the opinion of the
transplant team, would keep the patient from complying with the needs of the protocol
and/or would markedly increase the morbidity and mortality from the procedure.

- The candidate has any conditions, in the opinion of the transplant team, such as
substance abuse, or severe personality disorder that would keep the patient from
complying with the needs of the protocol and would markedly increase the morbidity
and mortality from the procedure.