In this paper a partition line is used in the counterflow system to present the default (conventional) traffic rule: pedestrians prefer to walk on a certain side on the road during movement, e.g., the right-hand side in China or the left-hand side in Japan. Based on the counterflow model of Takimoto (model A), we introduced two modified models, i.e., model B and C, to study the effects of a partition line in the consideration of people who do not obey the default traffic rule. Model B represents that factor in time scale, while model C in space scale. In model B, there are pedestrians who cross the partition line but choose not to obey the default traffic rule with a probability p(nor), while in model C, if a pedestrian crosses the partition line and goes away from it further than a certain nonobeying-rule threshold distance d(t), he will not obey the traffic rule. It is found that the behavior of traffic rule breaking influences much the counterflow when it is at the choking flow state rather than at the free moving or stopped state. Furthermore, it is shown that the default traffic rule is not always positive to the counterflow in all situations. It depends on the game result of these two opposite sides: to use the channel width as much as possible and to avoid the interference from the other group as far as possible.