Numerical extraction of complex refractive index of an unknown absorbing layer inside a multilayer sample from ellipsometry measurement is discussed. The approach of point by point extraction considering all points of spectroscopic data as independent data points is investigated. This problem has typically multiple solutions and the standard method consisting in fitting calculated to experimental point is likely to converge to a wrong solution if a precise guess value is not given. An alternate method is proposed, based on the determination of contours of the ellipsometric function, to provide all solutions in an as extended as wanted range of complex refractive index values. The method is tested through different kinds of sample examples. Errors relative to any of the parameters used in the sample model are calculated and discussed. This method should be helpful in many practical cases of ellipsometry data interpretation. (C) 2012 Elsevier B.V. All rights reserved.