A method has been developed to determine the thickness and the wavelength-dependent refractive indices and absorption coefficients of thin optical films by fitting a five parameter function to measured transmission spectra. Initial values for the fitting parameter are obtained from the transmission values at the spectral maxima and minima of the interference patterns created by the films. This is followed by a systematic variation of those parameters which can cause a failure of the calculation by reaching local minima of The residual sum of squares. The final fitting is performed with a Marquardt algorithm. A Monte Carlo simulation has indicated that the accuracy of this method is at least one order of magnitude better than that of the methods utilising only the interference extrema.