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A new method is proposed to calculate the Grüneisen parameter directly from the experimental Hugoniot data, without any assumption on the lattice vibrational mode of the material being studied. Compared with the three distinguishable features that support the rationality of the method. A new phenomenon that the lattice vibrational mode changes with the thermodynamic state of the solid has been first observed from the calculated results, which implies that the material parameter g, characterizing the lattice vibrational mode, is material dependent rather than a material constant.