The study medication, rivaroxaban, is an oral (by mouth) medication. Rivaroxaban directly inhibits one of the clotting mechanisms in the blood that is involved in the formation of blood clots in the veins in the body. The ability to inhibit blood clotting will be measured. Rivaroxaban is currently approved in the European Union by the European Medicines Agency (EMEA) for the prevention of blood clots in veins in orthopedic (bone) surgical patients who have had elective total joint (hip or knee) replacement. It is currently under review by the Food and Drug Administration (FDA) in the United States for this same indication. Enoxaparin is a medication that is injected into the fat tissue under the skin and is approved by the FDA for the treatment and prevention of blood clot formation in the veins. The goal of the study is to describe the short-term effects that the study drug has on the body when a patient is switched from enoxaparin to rivaroxaban. The study hypothesis, or theory, is that when switched from enoxaparin to rivaroxaban the ability of the body to inhibit blood clotting activity will continue. This is an open-label study which means that all persons involved in the study will know what study drug is being given to them. It is a single-arm study which means that all patients will be administered the same study medication, rivaroxaban. The study will be conducted at large orthopedic centers in the United States. All patients will have had elective total hip or total knee replacement surgery. While in the hospital, eligible patients will have been receiving enoxaparin either 30 mg twice a day or 40 mg once daily. Upon discharge from the hospital all eligible patients will require a stay in a subacute unit and continuing medication for blood clot prevention. After providing written informed consent, patients will have screening procedures completed to determine eligibility. Safety evaluations at the screening procedure will include a physical examination, vital signs, and clinical blood laboratory tests. Women, who are able to bear children, will also have a screening blood pregnancy test performed. A negative pregnancy test is needed to be in the study. Just before receiving the first dose of rivaroxaban, 10 mg, blood sampling for the short-term effects of rivaroxaban will begin and continue at various times. All patients will receive 10 mg of rivaroxaban daily. In addition, the study doctor will do an assessment of the surgical wound. At the time of discharge from the subacute unit, if the study doctor feels it is appropriate, an adequate supply of rivaroxaban will be provided to complete the full course of therapy. If a patient withdraws his/her consent prior to completion of the study, the appropriate course of blood clot prevention therapy will be prescribed by the study doctor. Upon completion of rivaroxaban therapy, all patients will be required to have final study procedures performed. Those patients who continue oral rivaroxaban after discharge from the subacute unit will be required to return for an office visit for final study procedures either at the time of completion of rivaroxaban therapy or at the surgical follow-up visit. Patients who have rivaroxaban discontinued prior to discharge from the subacute unit will have final study procedures completed at that time and a subsequent office visit will not be required. In all cases, the prescribed rivaroxaban therapy must have been completed prior to the time of the final visit. Safety evaluations at the final visit will include clinical laboratory blood tests, a physical examination, urine pregnancy test (if applicable), recording of any adverse events including details regarding any bleeding episodes or blood clot events, and assessment of the surgical wound. All patients will return any unused study medication and study participation will be complete. All patients will receive oral rivaroxaban 10mg daily. First dose of rivaroxaban will be given within 2 days after admission to the subacute unit, in the morning within 12 hrs (if 30mg twice a day) or 24 hours (if 40mg daily) of the enoxaparin dose. Patients will then continue to receive a daily 10 mg dose each morning. The total duration of combined therapy (enoxparin plus rivaroxaban) may not exceed 35 days for patients with total hip replacement or 14 days with total knee replacement.