Finding collision-free path from the starting point to the destination point is the primary objective for a robot navigating a workspace with obstacles. The obstacle avoidance algorithm presented in this paper is based upon the geometric modeling technique called quadtree. In our earlier work we have proposed an algorithm that selects a set of collision-free paths by analyzing the workspace-quadtree. Here, only those nodes that can allow collision-free pass for the mobile robot are selected. This paper investigates the effect of robot motion on the rotation of workspace-quadtree. It has been found that different rotations of the quadtree containing the same set of obstacles generate a different set of collision-free paths. A collision-free path, which is much shorter than the ones previously reported, can be obtained.