We report an upper limit on the flux of relativistic monopoles based on the nonobservation of in-ice showers by the Radio Ice Cherenkov Experiment (RICE) at the South Pole. We obtain a 95% C.L. limit of order 10(-18) (cm(2) s sr)(-1) for intermediate-mass monopoles of 10(7)<=gamma <= 10(12) at the anticipated energy E-tot=10(16) GeV. This bound is over an order of magnitude stronger than all previously published experimental limits for this range of boost parameters gamma and exceeds 2 orders of magnitude improvement over most of the range. We review the physics of radio detection, describe a Monte Carlo simulation including continuous and stochastic energy losses, and compare to previous experimental limits.
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