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We employ the exact solution given by G.D. Maliuzhinets (see Sov. Phys. Doklady, vol.3, p.752-5, 1958) for the canonical problem of diffraction of a plane wave by an arbitrarily angled impedance wedge to derive asymptotic approximations to the field components in a region contiguous to a face of the wedge. The asymptotic solution accounts for terms of order (kρ)-32/ (k is the wave number and ρ is the distance from the edge), is uniform with respect to observation and illumination aspects and includes the case of grazing illumination of a wedge face, which is known to be particularly difficult for high-frequency analysis (Uflmtsev's singularity).