In this paper, we propose a new method for the motion planning problem of rigid object dexterous manipulation with a robotic multi-fingered hand, under quasi-static movement assumption. This method computes both object and finger trajectories as well as the finger relocation sequence. Its specificity is to use a special structuring of the research space that allows to search for paths directly in the particular subspace GSn which is the subspace of all the grasps that can be achieved with n grasping fingers. The solving of the dexterous manipulation planning problem is based upon the exploration of this subspace. The proposed approach captures the connectivity of GSn in a graph structure. The answer of the manipulation planning query is then given by searching a path in the computed graph. Simulation experiments were conducted for different dexterous manipulation task examples to validate the proposed method.