An algorithm to characterise multilayer optical coatings with large numbers of layers by spectroscopic ellipsometry, using a discrete spectral-zone fitting approach, has been demonstrated by characterising a 27-layer TiO2/SiO2 multilayer beam combiner in the wavelength range of 280-1200 nm. The ellipsometric spectra are fitted first in the wavelength regime of 700-1200 nm and the sample structure was determined. TiO2 and SiO2 layers have been assumed to be transparent in this wavelength regime with dispersion-less refractive indices. The data were then fitted in the wavelength range of 280-340 nm to find the dispersion relation for the optical constants of TiO2. Finally, the fitting has been done in the wavelength range of 340-700 nm and the true dispersion of refractive index of TiO2 along with the best fit sample structure have been obtained.