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We propose a method to obtain characteristic curves, Riemann variables, and characteristic forms for a partial differential system of hyperbolic waves and a first order quasi-linear partial differential equations. The method is based on a construction of a left eigenvector of a matrix from eigenvalues of the matrix and some auxiliary matrixes, or some determinants. When applying to a system with no more than 4 dependent variable, the proposed method is numerically stable. An example of flood waves shows how to apply the proposed method.