Abstract : A new background rejection strategy for γ-ray astrophysics with stereoscopic Imaging Atmospheric Cherenkov Telescopes (IACT), based on Monte Carlo (MC) simulations and real background data from the H.E.S.S. [High Energy Stereoscopic System, see .] experiment, is described. The analysis is based on a multivariate combination of both previously-known and newly-derived discriminant variables using the physical shower properties, as well as its multiple images, for a total of eight variables. Two of these new variables are defined thanks to a new energy evaluation procedure, which is also presented here. The method allows an enhanced sensitivity with the current generation of ground-based Cherenkov telescopes to be achieved, and at the same time its main features of rapidity and flexibility allow an easy generalization to any type of IACT. The robustness against Night Sky Background (NSB) variations of this approach is tested with MC simulated events. The overall consistency of the analysis chain has been checked by comparison of the real γ-ray signal obtained from H.E.S.S. observations with MC simulations and through reconstruction of known source spectra. Finally, the performance has been evaluated by application to faint H.E.S.S. sources. The gain in sensitivity as compared to the best standard Hillas analysis ranges approximately from 1.2 to 1.8 depending on the source characteristics, which corresponds to an economy in observation time of a factor 1.4 to 3.2.