The metallic diffraction grating problem is solved forSpolarization using a conformal mapping and the surface impedance boundary condition. This completes the first differential formalism for diffraction gratings valid for good real conductors which does not require the fields inside the metal to be calculated. The method is used to calculate the electromagnetic fields diffracted by a cycloidal-groove grating. The numerical results are compared with those obtained using a rigorous formalism. It is shown that the method proposed here is particularly suited to the study of electromagnetic fields diffracted by a metallic grating, in the spectral zone corresponding to visible and infrared radiation where the conductivities of the metals generally used are high but finite.