This paper suggests an efficient approach to collision avoidance of a practical two-robot system. The approach is based on the C-space of one robot, and we consider only two and three dimensional C-space in which nearly all industrial manipulators can be reasonably represented for collision avoidance problems. The C-space of one robot is discretized with the concentric circles or spheres centered at the goal configuration. We then introduce the concept of free arc which is a set of the candidate configuration points on the concentric circle or sphere at each sampling time to avoid collisions. It is represented simply with respect to the coordinate frame attached to the goal configuration. The free arc is used as a tool for collision avoidance of a two-robot system and sub-optimality can be considered in determining a collision-free path. The main contribution of this paper is that it provides a method to construct C-obstacles in a time-varying environment more efficiently than the existing methods (e.g. slice projection method1) by restricting the search space at the expense of sacrificing completeness. Thus, it enables us to implement a practical collision avoidance algorithm for a two-robot system with decreased computational cost. Simulation results for two 2-d.o.f. manipulators and two PUMA robots are presented to show the efficacy of the proposed method.