The purpose of this study was to develop an automated method without user interaction for selecting the optimal data acquisition window in magnetic resonance coronary angiography (MRCA). The major problem in MRCA is the effective suppression of coronary motion resulting from respiration and cardiac contraction. To compensate for cardiac movement, data acquisition is generally limited to the period when the coronary artery is not moving, mainly during end-diastole, and is referred to as the cardiac rest period. Generally, the cardiac rest period is identified by the operator. Therefore, it is subjective and requires an experienced operator for accurate identification. As for the region of interest, the right coronary artery is known as an appropriate region for determining the cardiac rest period. Previous studies attempted to determine the position of coronary artery using template matching techniques or difference between the pixel intensities along frames of the cine images, but the detection accuracy of the cardiac rest period was not sufficiently high. In this study, we estimated the position of coronary artery using the mitral valve, tricuspid valve and the apex as known coordinates. Then, the position of the coronary artery was estimated with high accuracy using a template matching technique. In addition, we proposed a method to track the position of coronary artery in a cine image by updating the template to determine the cardiac rest period. As a result, automatic determination of the cardiac rest period was possible in 24 subjects.