A modified downhill simplex algorithm for single wavelength ellipsometry is presented, The algorithm finds the best-fitting solution (n, k, d) for a sample consisting of a single absorbing layer when ellipsometric data corresponding to different incidence angles (at least two) are available. The method is easy to be implemented numerically and gives i) very good convergence properties and ii) simple adaptability to different practical situations, such as those in which there are more than two angles of incidence or those in which several independent measurements have been made of the same incident angle.