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A simple and accurate extended Jones matrix representation for the twisted nematic liquid-crystal display at the oblique incidence was obtained for the first time. The results obtained by this extended Jones matrix representation are quite close to those obtained by the faster 4×4 matrix method with spectrum averaging to account for the nonzero bandwidth of the incident light. However, the computation time for the extended Jones matrix method is less than half that of the faster 4×4 matrix method without spectrum averaging. Furthermore, at normal incidence, this extended Jones matrix representation reduces to the ordinary Jones matrix representation.