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A new approach to solving the magnetic field integral equation (MFIE) for the current induced on a infinite perfectly conducting rough surface is presented. By splitting the propagator matrix into contributions from the left and from the right of the point of observation, a second kind integral equation can be formed with a new Born term and a new kernel. Following discretization of this new integral equation, the unknown currents can be determined more rapidly and with significantly less storage requirements than conventional LU decomposition; where the time saving factor is roughly N/3 where N is the number of current samples on the surface and the usual storage requirements associated with matrix inversion are eliminated. While the new Born term is usually adequate for scattered field calculations, the new discretized integral equation can be iterated to amy desired accuracy with no apparent convergence problems. Results are presented for one-dimensional rough surfaces with rms heights exceeding one wavelength and rms slopes exceeding 40° which illustrate the robustness of the new Born term.