A description is given of a new experiment to measure the muon electric dipole moment (EDM) to between sigma = 10(-24) e-cm and 10(-25) e-cm, which would be 5 to 6 orders of magnitude improvement over the current world average. Muons are stored in a magnetic ring. Precession due to Thomas precession and the magnetic moment are canceled with the proper combination of applied E and B fields. Only precession due to a non-vanishing EDM remains, resulting in a large amplification of the EDM signal. The method has general applicability to charged particles.