We present the continuous wavelet transform (CWT) method for determining the dispersion curves of the refractive index and extinction coefficient of absorbing thin films by using the transmittance spectrum in the visible and near infrared regions at room temperature. The CWT method is performed on the transmittance spectrum of an a - Si(1-x)C(x):H film, and the refractive index and extinction coefficient of the film are continuously determined and compared with the results of the envelope and fringe counting methods. Also the noise filter property of the method is depicted on a theoretically generated noisy signal. Finally, the error analyses of the CWT, envelope, and fringe counting methods are performed.