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For this paper, we first obtain the Riemann solutions for the one-dimensional non-isentropic Euler equations of extended Chaplygin gas. The solutions are composed of shock waves, contact discontinuity and rarefaction waves. Furthermore, the behavior of these solutions under the limiting conditions are considered. As a certain parameter tends to zero, we find that the Riemann solutions of the one-dimensional non-isentropic Euler equations for extended Chaplygin gas can be transformed into the solutions of the generalized Chaplygin gas unidirectional. Finally, we are done to verify that the theoretical analysis is accurate by using numerical simulation.