A modified annexin protein, preferably annexin V, is used to prevent thrombosis without increasing hemorrhage. Annexin binds to phosphatidylserine on the outer surface of cell membranes, thereby preventing binding of the prothrombinase complex necessary for thrombus formation. It does not, however, affect platelet aggregation necessary for hemostasis. The modified annexin molecule can be a homodimer of annexin, an annexin molecule coupled to one or more polyethylene glycol chains, or an annexin molecule coupled to another protein. By increasing the molecular weight of annexin, the modified annexin is made to remain in circulation for sufficient time to provide a sustained therapeutic effect.