In this article, we suggest a new linear function and prove that the MUSCL scheme would have second-order accuracy, if the function was used to approximate the initial-value distribution of flow variables in every mesh. The scheme is suitable for the Enlerian calculation when monotonicity condition and some dissipative mechanisms are introduced. We approximate the characteristic equations with shock jump relations near discontinuities and resolve the problem of using characteristic method in whole flowfield calculation. Finally, we present the numerical examples of Emery problem and a rocket jet problem.