A "resonance method" of measuring the electric dipole moment (EDM) of nuclei in storage rings is described, based on two new ideas: (1) Oscillating particles' velocities in resonance with spin precession, and (2) alternately producing two sub-beams with different betatron tunes-one sub-beam to amplify and thus make it easier to correct ring imperfections that produce false signals imitating EDM signals, and the other to make the EDM measurement.PACS numbers: 29.20Dh, 21.20.Ky.