Approximately 2 million people in North America take the anticoagulant warfarin to prevent stroke, heart attack, and other events related to blood clots. Warfarin needs to be stopped before a person undergoes surgery or certain procedures because it can cause dangerous amounts of bleeding during and after surgery. Some doctors give a low molecular weight heparin (LMWH) to patients during the 2-week period when participants are without the effects of warfarin. The LMWH has the same effect as warfarin, but it acts and then leaves the system more quickly than warfarin. However, the LMWH is expensive, may increase the risk of bleeding, and has not been proven effective. This study will determine the safety and efficacy of an LMWH in adults with atrial fibrillation who stop warfarin in preparation for surgery.