 This is a randomized participants are assigned to intervention groups by chance, open-label both physicians and participants know the identity of the assigned treatment, active-controlled, multi-center safety study of rivaroxaban or VKA before and after a catheter ablation procedure. This study requires collaboration with medical institutions that provide access to electrophysiologists who normally perform the catheter ablation procedure. In this study, NVAF is to be defined as the presence of AF in a person who does not have a prosthetic heart valve annuloplasty with or without prosthetic ring, commissurotomy andor valvuloplasty are permitted and who does not have hemodynamically significant mitral valve stenosis. Approximately 250 eligible participants, age 18 years or older, with a history of paroxysmal, persistent, or long standing persistent NVAF who are scheduled to undergo an elective catheter ablation procedure will be randomized in a 1:1 ratio to receive either rivaroxaban 20 mg orally, once-daily, administered preferably with the evening meal or VKA adjusted to achieve a recommended International Normalized Ratio of 2.0 to 3.0. 