An intravascular medical device having a structure shaped and sized for introduction into the vascular system of a patient including a base material and a coating of a thrombolytic agent on the base material. The thrombolytic agent advantageously dissolves or breaks up the formation of thrombus on the surface of the structure when placed in the vascular system of a patient. The intravascular medical device also includes a antithrombogenic agent for inhibiting the formation of thrombus on the surface of the medical device. The method of treating a medical device with a thrombolytic agent includes providing a base material for the medical device along with a thrombolytic agent. The base material is dipped into the thrombolytic agent and then removed to allow the thrombolytic agent to dry on the surface thereof. The dipping and drying steps are repeated to increase the concentration or quantity of the thrombolytic agent on the device.