The newly developed algorithm of evolving factor analysis has been supplemented by iterative refinement. It allows the completely model-free calculation of concentration profiles and spectra from spectrophotometric and other spectroscopic data. Not even implicit use is made of the law of mass action. The results are practically identical with those based on a specific chemical model and classical least-squares refinement. Iterative evolving factor analysis is based on applying factor analysis successively to the set of the first 1,2 cdots, three dots, centered M spectra of a spectrometric titration. The analysis is repeated from the opposite end and the eigenvalues thus calculated are combined into "concentration profiles" of completely abstract "species". These "concentration profiles" are iteratively refined by normalization, calculation of the absorption spectra from the normalized concentrations and recalculation of the concentration profiles from the absorption spectra. Evolving factor analysis is not restricted to spectrometric titrations, and can also be applied to peak resolution in chromatography using a multiwavelength (diode array) photometric or mass-spectrometric detection system, or to any other ordered set of multichannel data.