Three computational schemes for pseudoequivalent potential temperature (PEPT) are compared, the influences of PEPT on the computational accuracy of Showalter index (SI) are analyzed, and highaccuracy computation schemes of SI are proposed. First, the airparcel temperature and pressure at the lifted condensation level are calculated on the basis of the conservation property of potential temperature and mixing ratio during dry adiabatically lifting process. Then, Bolton formula is used to calculate the initial PEPT at 850 hPa. Next, Stackpole iteration algorithm is employed to look for the airparcel temperature at 500 hPa lifted adiabatically from 850 hPa keeping PEPT conservational, and thus SI can be finally solved. It is found that the computational error of PEPT constitutes an important part of the error of SI, therefore it is quite necessary to utilize accurate formula to compute PEPT. Comparison shows that the Bolton formula and LRC formula are more precise than the conventional Rossby formula to calculate PEPT. The PEPT at 850 hPa calculated by the classic Rossby formula is systematically lower than that using the other two formulas, and the error increases with the increasing of air temperature and humidity. Consequently, the mean absolute error of SI decreases from 0.66℃ using Rossby formula to 0.45℃ using Bolton formula. In comparison with the previous studies, the computation scheme proposed in this paper shows improved accuracy, feasibility in programming, and encouraging potential in operational practices of convective weather forecasting.