Based on the crystal lattices oscillator model, a thermodynamic equation of state is derived using a statistical dynamics method. The new parameter R of this equation of state is independent of the Grüneisen parameter, as compared with its predecessor, which was given by Q. Wu and F. Q. Jing. The calculated shock Hugoniot loci based on this new parameter are in good agreement with those calculated by the original parameter over a wide pressure range. This validates the new form of the R parameter.