Density functional theory with gradient corrections has been employed to study the reaction pathways and the reaction energetics for the transformations of CH4 to C and H on a Pd(100) surface. On examination of transition state structures identified in each elementary reaction, a clear relationship between the valencies of the CHx fragments and the locations of the transition states emerges. The higher the valency of the CHx fragment, the higher the coordination number of the CHx with the surface atoms. The calculated reaction energetics are in good agreement with the experiments. In addition, calculation results are also used to illustrate an interesting issue concerning the CH3 stability on Pd surfaces.