The zero order generalized Morse wavelet was proposed as a method to determine the refractive index and extinction coefficient dispersions of an absorbing thin film in the visible and near infrared regions at room temperature. The generalized Morse wavelet has two degree of freedom and the advantages and disadvantages of additional degree of freedom were discussed in the simulation works. The simulation studies were based on the mean relative error and Cauchy coefficients comparisions, and accuracy of the calculated refractive index was improved by the presented method, were compared with the Morlet wavelet and Paul wavelet. Also, the noise immunity of the method was discussed. The experimental validity of the method was tested on a cadmium sulfide absorbing thin film and the calculated refractive index were cross checked with the value of envelope method and literature.