We propose a new and simple procedure to overcome the ambiguity in the determination of optical constants of thin absorbing films from spectroscopic reflectance and transmittance measurements. The basis for the proposed method is an error analysis with the help of an error simulation technique and an error variation technique. We show that in practice (owing to experimental errors) it is not possible to overcome the problem of ambiguity by normal-incidence spectroscopic measurements alone. At least one oblique-incidence measurement is necessary for unambiguously determining the optical constants of the film. We discuss the consequences of experimental errors of the measured transmittance and reflectance values for the determination of the optical constants.