In this letter, a new strategy to enhance the discrimination of high energy gamma rays from the huge charged cosmic rays background in large cosmic rays ground arrays is presented. This strategy is based on the introduction of a new simple variable, Pγhα, which combines the probability of tagging muons and/or very energetic particles in each single array station. The discrimination power of this new variable, particularly important for and above multi-TeV energies, is illustrated for a few specific examples in the case of a hypothetical water Cherenkov detector cosmic ray array, both in the case of low and high particle stations occupancy. The results are very encouraging and hopefully will be demonstrated in the present and future gamma-ray Observatories.