Recent demands of the gear coupling are to reduce gear noise that is supposed to be caused by gear tooth gap for shaft angle fluctuation. In generally, large shaft angle increases tooth gap for shaft angle fluctuation. On the same time, load capacity is supposed to decrease. The tooth gap for shaft angle fluctuation is given by the analysis of tooth contact. The conventional analysis is an approximate one and is limited on its precision. An analysis of higher precision is necessary for recent critical demands on the gear coupling. This paper discusses analysis of clearance of matching tooth surface, where the profile of rack tooth surface has a straight line. Conact bearing pattern spreads in the direction to tooth tip and has edge contact. Those are different from the conventional assumptions.