We are proposing a new method to carry out a dedicated search for a permanent electric dipole moment (EDM) of the muon with a sensitivity at a level of 10(-24) e . cm in both statistics and systematics. This will make the sensitivity of the EDM experiment to non-standard physics better than the sensitivity of the present muon g-2 experiment, assuming the CP violating phase of the probed physics is of order one. The experimental design exploits the strong motional electric field sensed by relativistic particles in a magnetic storage ring.(1,2) As a key feature, a novel technique has been invented in which the g-2 precession is compensated with a radial electric field.