Inclusion Criteria:

          1. Patients with MDS (up to 20% blasts) of any risk. Patients with lower risk MDS (low
             and int-1 by IPSS) could have received prior non-hypomethylating agent therapy (ie
             growth factors or lenalidomide). Patients with higher risk MDS (int-2 or high by IPSS)
             should not have received prior therapy with a hypomethylating agent.

          2. Age 18 years or older.

          3. Adequate organ function: creatinine </=2.5 x Upper Limit of Normal (ULN); serum
             bilirubin </=2.5 x ULN; aspartate transaminase (AST) and alanine transaminase (ALT)
             </=2.5 x ULN.

          4. Eastern Cooperative Oncology Group (ECOG) performance status </=2.

          5. Females of childbearing potential must have a negative serum or urine beta human
             chorionic gonadotrophin (beta-hCG) pregnancy test result within 24 hours prior to the
             first dose of treatment and must agree to use an effective contraception to avoid
             pregnancy for 23 weeks (30 days plus the time required for nivolumab to undergo five
             half-lives) after the last dose of investigational drug. Females of non- childbearing
             potential are those who are postmenopausal greater than 1 year or who have had a
             bilateral tubal ligation or hysterectomy.

          6. Males who have partners of childbearing potential must agree to use an effective
             contraceptive method during the study and for 31 weeks after the last dose of
             nivolumab.

          7. Patients or their legally authorized representative must provide written informed
             consent.

        Exclusion Criteria:

          1. History of another primary invasive malignancy that has not been definitively treated
             or in remission for at least 2 years. Patients with non-melanoma skin cancers or with
             carcinomas in situ are eligible regardless of the time from diagnosis (including
             concomitant diagnoses).

          2. Any major surgery, radiotherapy, chemotherapy, biologic therapy, immunotherapy,
             experimental therapy within 2 weeks prior to the first dose of the study drugs.

          3. Patients with any other known concurrent severe and/or uncontrolled medical condition
             (e.g. uncontrolled diabetes; cardiovascular disease including congestive heart failure
             New York Heart Association (NYHA) Class III or IV, myocardial infarction within 6
             months, and poorly controlled hypertension; chronic renal failure; or active
             uncontrolled infection) which, in the opinion of the investigator could compromise
             participation in the study.

          4. Patients unwilling or unable to comply with the protocol.

          5. Patients who are on high dose steroid (ie prednisone or equivalent more than 10 mg a
             day) or immune suppression medications.

          6. Patients with autoimmune diseases (e.g., rheumatoid arthritis, systemic progressive
             sclerosis [scleroderma], Systemic Lupus Erythematosus, autoimmune vasculitis [e.g.,
             Wegener's Granulomatosis]).

          7. Patients with a history of Inflammatory Bowel Disease such as Crohn's disease and
             ulcerative colitis

          8. Patients known to be positive for hepatitis B surface antigen expression or with
             active hepatitis C infection (positive by polymerase chain reaction or on antiviral
             therapy for hepatitis C within the last 6 months) or with a history of HIV disease.

          9. Current therapy with other systemic anti-neoplastic or anti-neoplastic investigational
             agents.

         10. Females who are pregnant or lactating

         11. Prior treatment with stem cell transplantation.

         12. Prohibited Prior Treatments and/or Therapies: a) Prior therapy with an anti-KIR,
             anti-PD-1, or anti-PD-L1, antibody. b) Prior treatment regimens with any immune cell
             modulating antibody such as anti-CD137 and anti-OX40. However, prior anti-CTLA4
             therapy is allowed if the last dose is 101 days or more from the first dose of study
             drug. c) Exposure to any other investigational drug within 2 weeks prior to the first
             dose of study drug (within 101 days for anti-CTLA4 therapy). d) Any anti-cancer
             therapy (e.g., chemotherapy, biologics, vaccines, radiotherapy with curative intent,
             or hormonal treatment) within 2 weeks prior to the first dose of study drug
             administration (within 101 days for anti-CTLA4 therapy administration.

         13. Continued from #12: e) Use of non-oncology vaccines containing live virus for
             prevention of infectious diseases within 4 weeks prior to study drug. The use of the
             inactivated seasonal influenza vaccine (Fluzone®) is allowed. f) Systemic
             corticosteroid at immunosuppressive doses (> 10 mg/day of prednisone or equivalent),
             must be discontinued at least 2 weeks prior to enrollment.