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A nonlinear operator equation in terms of the operator of reflection by a plane periodic semi-infinite grating of thin metal strips is obtained for the H-polarized electromagnetic wave incidence. This equation is solved numerically for an incident plane wave. The algorithm created allows the solution of a nonlinear operator equation in the Fourier amplitude of the reflected field with the method of successive iterations. The initial approach chosen is substantiated, and the solution convergence is numerically verified. The field reflected by a semi-infinite grating is calculated and analyzed for different numerical values of the exciting wave angle of incidence, the strip width and the incident field wavelength.