Inclusion Criteria:

          -  One of the following diagnoses:

               -  MDS with International Prostate Symptom Score (IPSS) score of INT-1 or higher and
                  one of the following:

                    -  Symptomatic anemia with either hemoglobin < 10.0 g/dL or requiring red blood
                       cell (RBC) transfusion

                    -  Thrombocytopenia with a history of two or more platelet counts < 50,000/µL
                       or a significant hemorrhage requiring platelet transfusions

                    -  Neutropenia with two or more absolute neutrophil count (ANC) < 1,000/µL

               -  Non-M3 AML

          -  Prior treatment with ≥ 4 cycles of a hypomethylating agent (decitabine or azacitidine)
             without response OR documented disease progression on or after hypomethylating agent
             therapy

          -  Age ≥ 18 years old

          -  Adequate renal and hepatic function defined as all of the following:

               -  total bilirubin ≤ 1.5 x upper limit of normal (ULN), except in cases of Gilbert's
                  disease

               -  aspartate aminotransferase (AST) and alanine aminotransferase (ALT) ≤ 2.5 x ULN

               -  serum creatinine < 2.0 x ULN

          -  Peripheral blood blast count < 10,000/ µL.

          -  Eastern Cooperative Oncology Group (ECOG) performance status ≤ 2

          -  Females must be surgically or biologically sterile or postmenopausal or, if of
             childbearing potential, must agree to use an adequate method of contraception during
             the study until 30 days after the last treatment. Males must be surgically or
             biologically sterile or agree to use an adequate method of contraception during the
             study until 30 days after the last treatment.

          -  Ability to understand and willingness to sign an IRB approved written informed consent
             document (or that of legally authorized representative, if applicable).

        Exclusion Criteria:

          -  Prior allogeneic stem cell transplant

          -  Central nervous system (CNS) leukemia

          -  Diagnosed with AML and eligible for standard induction chemotherapy or stem cell
             transplantation.

          -  At an increased risk of hemorrhage.

          -  Known allergies, hypersensitivity, or intolerance to any form of heparin or
             azacitidine

          -  Presence of significant active bleeding or condition requiring maintenance of a
             platelet count > 50,000/µL

          -  Presence of any condition requiring any form of anticoagulant therapy (heparin flushes
             for IV catheter are permitted)

          -  Receiving concomitant chemotherapy, radiation therapy, or immunotherapy during the
             duration of treatment on protocol, or within 21 days prior to enrollment

          -  Known seropositivity for or active viral infection with human immunodeficiency virus
             (HIV), hepatitis B virus (HBV), or hepatitis C virus (HCV). Patients who are
             seropositive because of hepatitis B virus vaccine are eligible.

          -  Uncontrolled intercurrent illness including, but not limited to, ongoing or active
             infection, symptomatic congestive heart failure, unstable angina pectoris, or cardiac
             arrhythmia

          -  Pregnant and/or breastfeeding. Women of childbearing potential must have a negative
             pregnancy test within 28 days of study entry.