Clements introduced a method for calculating the estimators of two classical process capability indices (PCI), Cp and Cpk, for non-normal Pearsonian populations. Pearn and Kotz applied Clements' method to obtain first approximation estimators of PCIs for non-normal populations to the two more advanced PCIs, Cpm and Cpmk developed by Chan et al. and Pearn et al. In this paper, we consider a different approach for calculating the estimators of the four PCIs. The new approach may be viewed as a modification of Clements' method. Comparisons between Clements' and the proposed new methods are also provided.