Methods of thrombolysis that allow the use of a fibrinolytic composition comprising reversibly inactivated acidified plasmin and the localized delivery of the plasmin to a vascular thrombotic occlusion are disclosed. Further disclosed is a method for administering a therapeutic dose of a fibrinolytic composition substantially free of plasminogen activator to a human or animal having a vascular thrombotic occlusion. The fibrinolytic composition includes a reversibly inactivated acidified plasmin substantially free of plasminogen activator. Intravascular catheter delivery of the fibrinolytic composition directly into or in the immediate vicinity of the thrombus is disclosed to minimize the systemic degradation of fibrin while retaining the maximum plasmin activity against the thrombus. The method is applicable to the dissolution of thrombi in artificial devices, e.g., hemodialysis grafts.