This is a phase 2 trial to evaluate the safety of adoptive immunotherapy with Non-Inherited
      Maternal Antigen (NIMA) compatible, Inherited Paternal Antigen (IPA) targeted CBU or with
      haplo-identical stem cells after conventional induction therapy for very high risk Acute
      Myeloid Leukemia (AML) or Myelodysplastic Syndrome (MDS).

      The study has 2 cohorts - patients in cohort 1 will receive CBU cells as adoptive
      immunotherapy. Patients in cohort 2 will receive haplo-identical cells. Both cohorts will be
      evaluated separately and no formal statistical comparison between cohorts will be performed.

      There will be approximately 20 patients in each cohort, and a 95% confidence interval for the
      proportion of patients experiencing grade III-IV GVHD complications or unexplained prolonged
      myelosuppression complications in each cohort can be constructed to be within +/- 13.1% of
      the observed complication proportions. This calculation assumes an expected prevalence of
      each of these complication proportions of no greater than 10%.

      After 10 patients are enrolled in each group, the incidence of the above-defined
      life-threatening complications will be assessed. If more than one patient out of 10 enrolled
      patients (i.e., greater than 10%) in a cohort experiences either of these complications, the
      cohort will be stopped for safety.

      All potential recipients will have complete HLA typing and determination of HLA antibodies.
      An appropriate umbilical cord blood unit (CBU) will be identified or in the absence of an
      appropriate CBU, a haplo-identical donor will be identified.

      Treatment will be as per the treating physician's choice..

      The umbilical cord graft or haplo-graft will be administered between 24 - 72 hours after the
      completion of the chemotherapy regimen.

      The Graft Selection Algorithm is as follows:

        1. CBU Unit 5/6 Matched - 1 NIMA match with patient

        2. CBU Unit 5/6 Matched - Shared IPA target(s) with patient

        3. Haplo-identical relative

        4. CBU Unit 4/6 Matched - 1-2 NIMA matches with patient

        5. CBU Unit 4/6 Matched - Shared IPA target(s) with patient

      Within 42 days of transplant, the recipient's pre-treatment evaluation includes: medical
      history and physical examinations, Eastern Cooperative Group Oncology Group (ECOG) score,
      complete blood count (CBC), HLA antibodies, and cytomegalovirus (CMV) antibody testing.

      Patients will continue with the therapy specified in this protocol until one of the following
      occurs:

        -  Achievement of protocol endpoint complete remission (CR) or CR with incomplete platelet
           recovery (CRp) after induction and cellular therapy;

        -  Failure to achieve CR or CRp; or,

        -  Extraordinary Medical Circumstances: If, at any time the constraints of this protocol
           are detrimental to the patient's health and/or the patient no longer wishes to continue
           protocol therapy, remove the patient from protocol treatment. In this event.

      After removal from protocol therapy, patients will continue to be followed for survival and
      disease status. Samples for correlative studies will continue to be collected every two
      months until one year after cell infusion.