This is a phase II study to determine the response to suramin of previously untreated metastatic melanoma, and to evaluate the safety and toxicity of this agent. It is anticipated that 29 patients will enter this single center study. Suramin will be infused via a peripheral vein or permanent central venous access device. The initial dose will be infused over 2 hours; all subsequent doses will be administered over one hour. All patients will have a 12 week break between cycle #1 and cycle #2.