The purpose of this research study is to determine the safety of using the study drugs bevacizumab and ipilimumab together, and the doses in combination which can be given to people safely. This study also seeks to investigate whether using both study drugs lengthens the amount of time before the participants melanoma worsens.

• There are two phases to this research study, Induction Phase and Maintenance Phase.
• Induction Phase: Participants will receive ipilimumab by an infusion into a vein or central line at weeks 1, 4, 7 and 10 for a total of 4 infusions. Bevacizumab is also given as an infusion into a vein or central line at weeks 1, 4, 7 and 10 along with ipilimumab and then every 3 weeks by itself. During all cycles of study therapy, the participant will have a physical exam on the first day and undergo blood tests at every study visit. At weeks 1, 4, 7, 10 and 12 a urine sample will be obtained for analysis.
• Chest, abdomen and pelvic CT scans will be performed at week 12. If the scans at week 12 show that the participants cancer has remained stable or decreased, they will be asked to have repeat CT scans in three months.
• Positron Emission Tomography (PET) scans will be done at week 8 and week 16.
• Maintenance Phase: If the scans performed at week 12 show the cancer has improved or stayed the same, then the participant will continue to receive bevacizumab every three weeks and undergo a CT scan every 3 months. Also, every 3 months the participant may be eligible to receive additional doses of ipilimumab in addition to the bevacizumab.

Inclusion Criteria:

• Measurable unresectable Stage III or Stage IV melanoma
• ECOG Performance Status 0 or 1
• 4 weeks or greater since treatment
• Must have recovered from any acute toxicity associated with prior therapy
• Life expectancy of greater than 12 weeks
• 18 years of age or older
• Laboratory values as outlined in protocol
• Negative screening tests for HIV, active Hepatitis B and Hepatitis C
• Patients who received prior therapy with anthracyclines should have a baseline MUGA or echo with a normal ejection fraction

Exclusion Criteria:

• CNS metastases
• Pregnant or nursing women
• Prior therapy with bevacizumab or ipilimumab
• Active infection
• Autoimmune disease: Patients with a history of inflammatory bowel disease are excluded from this study as are patients with a history of symptomatic autoimmune disease
• Any other malignancy from which the patient has been disease-free for less than 5 years, with the exception of adequately treated and cured basal or squamous cell skin cancer, superficial bladder cancer or carcinoma in situ of the cervix
• Any underlying medical condition which, in the principal investigator's opinion, will make the administration of study drug hazardous or obscure the interpretation of adverse events
• Any concurrent medical condition requiring the use of systemic steroids
• Inadequately controlled hypertension
• Any prior history of hypertensive crisis or hypertensive encephalopathy
• NYHA Grade II or greater congestive heart failure
• History of myocardial infarction or unstable angina within 6 months prior to study enrollment
• History of stroke of transient ischemic attack within 6 months prior to study enrollment
• Significant known vascular disease
• Symptomatic peripheral vascular disease
• Evidence of bleeding diathesis or coagulopathy
• Major surgical procedure or significant traumatic injury within 28 days prior to study enrollment
• Core biopsy or other minor surgical procedure, excluding placement of a vascular access device, within 7 days prior to study enrollment
• History of abdominal fistula, gastrointestinal perforation, or intra-abdominal abscess within 6 months prior to study enrollment
• Serious, non-healing wound, ulcer or bone fracture
• Proteinuria at screening
• Known hypersensitivity to any component of bevacizumab
• History of hemoptysis within 3 months prior to study enrollment
• Current, ongoing treatment with full-dose warfarin or its equivalent
• Current or recent (within 10 days of enrollment) use of aspirin (>325mg/day) or chronic use of other NSAIDs
• Medications that inhibit platelet function
• Known involvement of melanoma within gastrointestinal tract
• Ulcerated skin lesions