A Study of Combination with TBI-1401(HF10) and Ipilimumab in Japanese Patients with Unresectable or Metastatic Melanoma

Inclusion Criteria: * Patients with histologically confirmed Stage IIIB, IIIC or IV unresectable or metastatic melanoma except uveal melanoma, who must have a history of treatment (chemotherapy, molecular targeted therapy, or anti PD-1 antibody therapy). * Patients must have measurable non-visceral lesion(s) that are evaluable by the modified World Health Organization (mWHO) criteria and immune-related response criteria (irRC). * Patients must be ≥ 20 years of age. * Patients must have a life expectancy ≥ 24 weeks. * Patients must have an Eastern Cooperative Oncology Group (ECOG) performance status of 0, 1, or 2. * Patients must have adequate organ function, defined as * Total bilirubin levels ≤ 1.5 x upper limit of normal \[ULN\] (except for patients with Gilbert's Syndrome, who must have a total bilirubin of less than 3.0 mg/dL) * AST/ALT levels ≤ 2.5 x ULN, or ≤ 5 x ULN if liver metastases are present. * Creatinine ≤ 1.5 x ULN or creatinine clearance (calculated) ≥ 60 mL/min/1.73 m\^2 for patients with creatinine \> 1.5 x ULN. * Absolute neutrophil count ≥1,500/µL and * Platelet count ≥ 75,000/ µL * Men and women of childbearing potential must agree to use adequate contraception from the time of consent through 30 days after final study treatment. * Females of childbearing potential must have a negative urine or serum pregnancy test within 1 week prior to start of treatment. * Patients must be able to understand and willing to sign a written informed consent document. Exclusion Criteria: * Patients who were previously treated with ipilimumab by intravenous infusion. * Patients receiving chemotherapy or molecularly targeted drug or anti-PD-1 antibody treatment or radiotherapy or immunotherapy within 4 weeks prior to initiating study treatment. * Patients with a history of Grade 4 adverse events caused by chemotherapy, molecularly targeted drug, anti-PD-1 antibody treatment, radiotherapy or immunotherapy conducted more than 4 weeks prior to TBI-1401(HF10) treatment, or presence of such adverse events of Grade 2 or greater, except alopecia and adverse events controlled by a treatment. * Patients receiving anti-herpes medication within 1 week prior to initiating TBI-1401(HF10) administration, except local treatment such as ointment. * Patients with a history of significant tumor bleeding, or coagulation or bleeding disorders. * Patients with target tumors that could potentially invade a major vascular structure (e.g., innominate artery, carotid artery), based on unequivocal imaging findings. * Patients with Grade 2 or greater neurologic abnormalities (CTCAE version 4.0), including Grade 2 or greater peripheral neuropathy caused by previous treatments. * Patients with clinically evident Human Immunodeficiency Virus (HIV), Hepatitis B Virus (HBV), Hepatitis C virus (HCV), or Epstein-Barr virus (EBV) infection. * Patients requiring systemic glucocorticoid (except 10 mg/day/body prednisolone or less) or immunosuppressive therapy because of the presence or history of autoimmune disease (e.g., Crohn's disease, ulcerative colitis) or other diseases. * Concurrent use of any other investigational agents within 4 weeks prior to initiating study treatment. * Patients with active CNS metastases or carcinomatous meningitis, except patients with CNS lesions that have been treated and have no evidence of progression in the brain on CT/MRI for ≥ 3 months. * Pregnant or breastfeeding women (excluding the case in which breastfeeding is discontinued and will not resume it); women desiring to become pregnant within the timeframe of the study are also excluded. * 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 that would limit compliance with study requirements, as determined by the investigator.