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The object of this paper is to present a coordinate-free method in solving the problem of wave reflection from the surface of an anisotropic medium. Based on the direct manipulation of vectors, dyadics, and their invariants, the method eliminates the use of coordinate systems. It facilitates solutions and provides results in a greater generality. The paper contains the following results in coordinate-free forms: (1) the dispersion equation, (2) the laws of reflection and refraction, (3) the Booker quartic equation, and (4) the transmission and reflection coefficient matrices.