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This paper studies diffraction of an obliquely incident, arbitrarily polarized plane electromagnetic wave by an anisotropic impedance wedge with an opening angle 2Φ between 0 and 2π, and presents a closed-form exact solution to a class of impedance wedge faces and the related uniform asymptotic solution (UAS). On use of a unitary similarity transform, the boundary conditions on the wedge faces is brought into a form, which makes the exactly soluble class of impedance faces evident. The exact solution is found with help of the Sommerfeld-Malyuzhinets (1896, 1958) technique, a generalized Malyuzhinets function χΦ and the so-called S-integrals. A standard procedure yields therefrom the UAS. The exact solution agrees with known analytical results in special cases, and the numerical results of UAS are confirmed by that of parabolic equation method (PEM).