We apply our recently proposed proper quantization rule, (x)]/h to obtain the energy spectrum of the modified Rosen-Morse potential. The beauty and symmetry of this proper rule come from its meaning-whenever the number of the nodes of φ(x) or the number of the nodes of the wave function ψ(x) increases by one, the momentum integralx Bx A k(x)dx will increase by π . Based on this new approach, we present a vibrational high temperature partition function in order to study thermodynamic functions such as the vibrational mean energy U , specific heat C, free energy F and entropy S. It is surprising to note that the specific heat C(k = 1) first increases with β and arrives to the maximum value and then decreases with it. However, it is shown that the entropy S(k = 1) first increases with the deepness of potential well λ and then decreases with it.