This is a multicenter, open-label (all people know the identity of the intervention), single-arm study. It will consist of 2 Phases: a Screening Phase (up to 21 days before the first dose administration), and Treatment Phase (for patients meeting the continuation criteria). During the Treatment Phase, patients will receive a dose of 1.5 mg/m2 trabectedin intravenous formulation administered as a 24-hour infusion on Day 1 of each suggested 21-day treatment cycle. All patients will receive 20 mg dexamethasone (or corticosteroid equivalent to dexamethasone). Number of cycles is not specified for this study. Patients may continue to receive treatment as long as they obtain an overall clinical benefit, ie, until there is clear evidence of disease progression or unacceptable toxicity, as judged by the investigator. Trabectedin is the first of a new class of antitumor agents. Previous studies with trabectedin in patients who had been previously treated for soft tissue sarcoma have suggested that treatment with trabectedin resulted in tumor shrinkage, disease stabilization, and improved survival rates. However, hematologic toxicity, hepatic toxicity, and renal impairment were also observed in these patients. The safety profile of trabectedin will be evaluated to further assess the potential risks of trabectedin treatment in patients previously treated for soft tissue sarcoma who are not expected to benefit from currently available therapeutic options for treatment of soft tissue sarcoma. Safety will be monitored throughout the study.