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The problem of diffraction by a thin cone is considered. The parabolic equation of diffraction theory is used as the governing equation. Authors introduce the method of a boundary integral equation for the parabolic equation. The integral equation is derived by applying the Green’s theorem. The kernel of the equation has a difference form,so the equation can be solved analytically using Fourier transform. As the result,some known formulae can be re-derived. Also,the integral equation can be solved numerically by iterations.