A new method for the detection of the electron electric dipole moment (EDM) using a solid is described. The method involves the measurement of a voltage induced across the solid by the alignment of the sample's magnetic dipoles in an applied magnetic field, H. A first application of the method to GdIG has resulted in a limit on the electron EDM of 5 x 10(-24)e cm, which is a factor of 40 below the limit obtained from the only previous solid-state EDM experiment. The result is limited by the imperfect discrimination of an unexpectedly large voltage that is even upon the reversal of the sample magnetization.