Inclusion Criteria:

   - All patients must have disease-free status documented by a complete physical
   examination and imaging studies within 4 weeks prior to randomization; imaging studies
   must include a total body positron emission tomography (PET)-computed tomography (CT)
   scan (with or without brain) and brain magnetic resonance imaging (MRI) or CT (if MRI
   is contraindicated); if PET-CT cannot be done, CT of neck, chest, abdomen, and pelvis
   should be done

      - If for some reason a CT cannot be done, an MRI may be done instead; any other
      imaging studies if performed (eg, bone scan) must show no evidence of disease

   - Patients must have primary cutaneous melanoma that belong to one of the following
   American Joint Commission on Cancer (AJCC) stages (2009 AJCC Melanoma Staging System):

      - Stage IIIB

         - T1-4b N1a M0

         - T1-4b N2a M0

         - T1-4b N1b M0

         - T1-4b N2b M0

         - T1-4b N2c M0

      - Stage IIIC

         - T1-4b N1b M0

         - T1-4b N2b M0

         - T1-4b N2c M0

         - Any T N3 M0

      - Stage IV

         - M1a

         - M1b

         - NOTE: patients with stage IV melanoma must have normal lactate dehydrogenase
         (LDH) and either distant skin, subcutaneous, lymph node, or lung metastases,
         but no other visceral metastases in order to be eligible; for patients with
         resected stage IV melanoma, LDH within the institutional upper limit of
         normal (ULN) must be documented within 4 weeks prior to randomization

   - Patients with disease recurrence after adequate surgical excision of the original
   primary cutaneous/unknown primary melanoma are allowed even if they don't fit the
   strict staging criteria, but only as follows:

      - Recurrence in a regional lymph node basin after a prior complete lymph node
      dissection; relapsed disease must be completely surgically resected with free
      margins

      - Recurrence in the form of in-transit or satellite metastases or distant
      skin/subcutaneous, nodal, or lung metastases that are completely surgically
      resected with free margins

      - Recurrence in a regional lymph node basin; relapsed disease must be completely
      surgically resected with free margins

   - Patients with unknown primary melanoma (Tx) who present with cutaneous, subcutaneous,
   nodal and/or lung metastases that are completely surgically resected with free margins
   are allowed; these patients are allowed even if they don't fit the strict staging
   criteria; for stage IV patients LDH within the institutional ULN must be documented
   within 4 weeks prior to randomization (M1c is not eligible)

      - NOTE: all subjects should be classified as IIIB, IIIC, M1a or M1b including
      subjects with disease recurrence after adequate surgical excision of the original
      primary melanoma; that is the treating team/physician investigator should review
      an overall TNM status (that includes primary tumor presentation and disease
      recurrence status) and provide a designation of IIIB, IIIC, M1a or M1b

   - Patients must be randomized within 84 days (12 weeks) of surgical resection; if more
   than one surgical procedure is required to render the patient disease-free, the
   patient must be randomized within 12 weeks of the last surgery

      - NOTE: patients with clinically positive lymph nodes for melanoma involvement or
      those with positive lymph nodes identified through lymphoscintigraphic and/or dye
      lymphographic techniques in the groin, axilla, or neck should have additional
      lymphadenectomy in those sites; the complete lymph node dissection procedure
      would be considered as the last surgery in counting the 84 days unless a
      subsequent surgical procedure(s) was clinically required to ensure the disease
      free status

   - Patients must have Eastern Cooperative Oncology Group (ECOG) performance status of 0-1

   - Patients should be carefully screened for depression at baseline and if there are
   indications or a history of depression it is strongly recommended that these patients
   be closely followed together with behavioral health or psychiatric medical support

   - All females of childbearing potential must have a blood test or urine study during
   screening to rule out pregnancy

   - Woman of childbearing potential (WOCBP) must be using an adequate method of
   contraception to avoid pregnancy throughout the study and for up to 26 weeks after the
   last dose of ipilimumab or HDI, in such a manner that the risk of pregnancy is
   minimized; women who are using oral contraceptives, other hormonal contraceptives
   (vaginal products, skin patches, or implanted or injectable products), or mechanical
   products such as an intrauterine device or barrier methods (diaphragm, condoms,
   spermicides) to prevent pregnancy, or are practicing abstinence or where their partner
   is sterile (e.g., vasectomy) should be considered to be of childbearing potential

      - Men of fathering potential and WOCBP must be using an adequate method of
      contraception to avoid conception/pregnancy throughout the study and for up to 26
      weeks after the last dose of ipilimumab or HDI in such a manner that the risk of
      pregnancy is minimized

   - White blood cell (WBC) >= 3,000/uL (obtained within 4 weeks prior to randomization)

   - Absolute neutrophil count (ANC) >= 1,500/uL (obtained within 4 weeks prior to
   randomization)

   - Platelets >= 100 x 10^3/uL (obtained within 4 weeks prior to randomization)

   - Hemoglobin >= 10 g/dL (obtained within 4 weeks prior to randomization)

   - Serum creatinine =< 1.5 mg/dL (obtained within 4 weeks prior to randomization)

   - Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) =< 2.5 x ULN (obtained
   within 4 weeks prior to randomization)

   - Serum bilirubin =< 1.5 x ULN, (except patients with Gilbert's syndrome, who must have
   a total bilirubin less than 3.0 mg/dL) (obtained within 4 weeks prior to
   randomization)

Exclusion Criteria:

   - Prior adjuvant treatment (chemotherapy, biotherapy, or limb perfusion) after the
   resection(s) that make(s) them eligible for this trial

      - NOTE: previous radiation therapy, including after the surgical resection, is
      allowed as long as 21 days have elapsed between the radiation and initiation of
      this adjuvant systemic therapy

   - Prior treatment with anti-cytotoxic T-lymphocyte antigen 4 (CTLA4) monoclonal
   antibodies or prior CTLA-4 inhibitor or agonist or prior clusters of differentiation
   (CD)137 agonist or prior interferon-alfa

      - Other forms of prior treatment for melanoma (e.g., aldesleukin [IL-2], anti-tumor
      vaccine, chemotherapy) are allowed if given before the resection(s) that make(s)
      the patient eligible for this trial, but these must have been completed at least
      4 weeks prior to randomization

   - Active infection requiring current treatment with parenteral antibiotics

   - Other significant medical, surgical, or psychiatric conditions or require any
   medication or treatment that in the opinion of the investigator may interfere with
   compliance, make the administration of ipilimumab or HDI hazardous or obscure the
   interpretation of adverse events (AEs), such as a condition associated with frequent
   diarrhea; patients with a baseline of frequent diarrhea (e.g. irritable bowel
   syndrome) are not eligible

   - Patients with an established diagnosis of depression that, in the assessment of the
   investigator may make the administration of interferon (IFN)-alfa or ipilimumab
   hazardous, should not be enrolled on this protocol; the risks and benefits of being
   treated with standard adjuvant IFN-alfa should be weighed very carefully in
   consultation with behavioral health or psychiatry

   - Documented history of inflammatory bowel disease (including ulcerative colitis and
   Crohn's disease) or diverticulitis (history of diverticulosis is allowed)

   - Autoimmune disorders or conditions of immunosuppression that require current ongoing
   treatment with systemic corticosteroids (or other systemic immunosuppressants),
   including oral steroids (i.e., prednisone, dexamethasone) or continuous use of topical
   steroid creams or ointments or ophthalmologic steroids; a history of occasional (but
   not continuous) use of steroid inhalers is allowed; replacement doses of steroids for
   patients with adrenal insufficiency are allowed; patients who discontinue use of these
   classes of medication for at least 2 weeks prior to randomization are eligible if, in
   the judgment of the treating physician investigator, the patient is not likely to
   require resumption of treatment with these classes of drugs during the study

      - Exclusion from this study also includes patients with a history of symptomatic
      autoimmune disease (e.g., rheumatoid arthritis, systemic progressive sclerosis
      [scleroderma], systemic lupus erythematosus, Sjögren's syndrome, autoimmune
      vasculitis [e.g., Wegener's granulomatosis]); motor neuropathy considered of
      autoimmune origin (e.g., Guillain-Barre syndrome and Myasthenia Gravis); other
      central nervous system (CNS) autoimmune disease (e.g., poliomyelitis, multiple
      sclerosis)

      - Patients with autoimmune hypothyroid disease or type I diabetes on replacement
      treatment are eligible

   - Prior infectious disease vaccination (e.g., standard influenza, H1N1 influenza,
   pneumococcal, meningococcal, or tetanus toxoid) within 4 weeks prior to randomization

   - Prisoners or subjects who are compulsorily detained (involuntarily incarcerated) for
   treatment of either a psychiatric or physical (e.g., infectious) illness

   - Other current malignancies are not eligible; patients with other malignancies are
   eligible if they have been continuously disease free for > 5 years prior to the time
   of randomization; patients with prior history at any time of any in situ cancer,
   lobular carcinoma of the breast in situ, cervical cancer in situ, atypical melanocytic
   hyperplasia or melanoma in situ are eligible; patients with prior history of basal or
   squamous skin cancer are eligible; patients who have had multiple primary melanomas
   are eligible

   - Pregnant or breast-feeding

      - NOTE: a woman of childbearing potential (WOCBP) is any woman, regardless of
      sexual orientation or whether they have undergone tubal ligation, who meets the
      following criteria: 1) has not undergone a hysterectomy or bilateral
      oophorectomy; or 2) has not been naturally postmenopausal for at least 24
      consecutive months (i.e., has had menses at any time in the preceding 24
      consecutive months); post-menopause is defined as:

         - Amenorrhea >= 12 consecutive months without another cause, or

         - For women with irregular menstrual periods and taking hormone replacement
         therapy (HRT), a documented serum follicle stimulating hormone (FSH) level
         >= 35 mIU/mL ; men or WOCBP who are unwilling or unable to strictly follow
         this requirement are not eligible

   - A positive pregnancy test at baseline

   - Active or chronic infection with human immunodeficiency virus (HIV), hepatitis B, or
   hepatitis C; patients must have negative testing for HIV, hepatitis B virus (HBV),
   hepatitis C virus (HCV) within 4 weeks prior to randomization