Inclusion Criteria:
* At least 18 years of age
* Eastern Cooperative Oncology Group (ECOG) performance status ≤ 2
* Diagnosis of hematologic malignancy (i.e. acute myeloid leukemia, acute lymphoblastic leukemia, chronic lymphocytic leukemia, chronic myelogenous leukemia, Hodgkin's lymphoma, non-Hodgkin's lymphoma, myelodysplastic syndrome, chronic myelomonocytic leukemia)
* Use of myeloablative or non-myeloablative conditioning regimen
* Use of mobilized peripheral blood stem cells from fully HLA-matched related or unrelated donor as a graft source
* Acute GvHD prophylaxis with methotrexate and tacrolimus
* Documented complete remission with full donor engraftment (by STR identity testing) on Day +30 bone marrow biopsy
* Complete remission: less than 5% blasts in an aspirate bone marrow sample with a count of at least 200 nucleated cells, no blasts with Auer rods or persistence of extramedullary disease PLUS absolute neutrophil count (ANC) \> 1,500/μL, platelet count ≥ 50,000/μL and no leukemic blasts in the peripheral blood.
* Negative minimal residual disease
* Full donor engraftment by STR testing (either by bone marrow or peripheral blood testing)
* Adequate end organ function:
* Serum bilirubin ≤ 1.5 x upper limit of normal (ULN)
* Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) ≤ 2.5 x ULN
* Creatinine clearance ≥ 40 mL/min/1.73 m\^2 by the Cockcroft-Gault formula
* Women of childbearing potential must agree to use adequate contraception (hormonal or barrier method of birth control, abstinence) prior to study entry, for the duration of study participation, and for 16 weeks after the last dose of study drug. Should a woman become pregnant or suspect she is pregnant while participating in this study, she must inform her treating physician immediately.
* Able to understand and willing to sign an Institutional Review Board (IRB)-approved written informed consent.
Exclusion Criteria:
* Active grade III-IV classic acute GvHD; subjects with prior resolved acute GvHD on stable doses of immunosuppression at time of enrollment will be permitted
* Evidence of classic chronic GvHD or overlap chronic GvHD at time of enrollment
* Subjects who participated in a clinical trial of acute GvHD prophylaxis in which chronic GvHD was a secondary end point
* Donor lymphocyte infusion administered to treat relapse or loss of donor chimerism
* Treatment with rituximab or other anti-B cell specific antibodies within previous 3 months
* History of other malignancy ≤ 5 years previous with the exception of basal cell or squamous cell carcinoma of the skin which were treated with local resection only or carcinoma in situ of the cervix
* Currently receiving any other investigational agents
* Known allergy or intolerance to any component of belimumab, including human or murine proteins or monoclonal antibodies
* Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations (including current drug or alcohol abuse or dependence, or history of drug or alcohol abuse or dependence within the last year) that would limit compliance with study requirements
* Use of parenteral (IV or IM) antibiotics (antibacterials, antivirals, anti-fungals, or anti-parasitic agents) within 14 days prior to planned start of therapy
* Evidence of serious suicide risk including any history of suicidal behavior in the last 6 months and/or any suicidal ideation in the last 2 months and/or poses a significant suicide risk in the judgment of the investigator
* History of pre-existing immunodeficiency disorder, autoimmune condition, or chronic infection
* Known HIV positivity
* Serologic evidence of current or past hepatitis B infection based on the results of testing for HBsAg and anti-HBc - Patients positive for HBsAg or HBcAb are excluded
* Positive test for hepatitis C antibody (patients with documented clearance of hepatitis C by PCR following treatment will be permitted)
* Currently on therapy for active chronic infection (such as tuberculosis, pneumocystis, cytomegalovirus, herpes simplex virus, herpes zoster and atypical mycobacteria). Prophylactic therapy is allowed.
* Has any other clinically significant abnormal laboratory value in the opinion of the investigator
