We present a recalibration of the two most recent analytical potential energy surfaces for the CH4 + H --> CH3 + H-2 reaction. Assuming a correct functional form, the recalibration process allows one to update the original parameters in light of new experimental and theoretical data. As calibration criteria we use the reactant and product experimental properties, and the most recent ab initio saddle-point properties, which differ from the original values, especially the imaginary frequency. For both modified surfaces we use rectilinear and curvilinear coordinates to calculate the vibrational frequencies at nonstationary points. The rate coefficients are calculated with variational transition-state theory and, in general, agree with the experimental data in the temperature range 300-1500 K. They present only a slight dependence on the modified surfaces used but a major dependence on the choice of coordinate system, especially at low temperatures where the rectilinear coordinates yield rate coefficients practically double those of the curvilinear ones. We also provide a detailed analysis of the kinetic isotope effects (KIEs) for the reverse reactions. All KIEs are "normal", i.e., the ratios of the unsubstituted/substituted rate coefficients are greater than unity and in good agreement with the experimental values. Both modified surfaces reproduce the experimental dependence of the KIEs on temperature, the agreement being best when curvilinear coordinates are used.