We present an automated procedure for the derivation of atmospheric parameters (Teff, log g, [M/H]) and individual chemical abundances from stellar spectra. The MATrix Inversion for Spectral SythEsis (MATISSE) algorithm determines a basis, Bθ(λ), allowing to derive a particular stellar parameter θ by projection of an observed spectrum. The Bθ(λ) function is determined from an optimal linear combination of theoretical spectra and it relates, in a quantitative way, the variations in the spectrum flux with variations in θ. An application of this method to the GAIA/RVS spectral range is described, together with its performances for different types of stars of various metallicities. Blind tests with synthetic spectra of randomly selected parameters and observed input spectra are also presented. The method gives rapid, accurate and stable results and it can be efficiently applied to the study of stellar populations through the analysis of large spectral data sets, including moderate to low signal to noise spectra.