An improved method for the discrimination of oils and fats is being proposed. The method is based on the principal component analysis and discrimination analysis of the results obtained by determination of the mole percentage of total fatty acids (fatty acid methyl esters analysis by GC) and regiospecific distribution of the same fatty acids in positions 1 and 3 of triglycerides (using a regiospecific lipase and analysis by GC of the produced butyl esters). Various samples (pure olive oils, various seed oils, mixtures of pure olive oils with seed oils, commercially available foods containing animal fats and/or vegetable oils and, finally, local pure olive oils from different areas of Greece) were subjected to two transesterification treatments. It was proved that the proposed method has a global discriminating ability of identifying (at a level of 5%) olive oil adulteration with various seed oils, discriminating animal fats from vegetable oils and animal fat adulteration with seed oils and, finally, discriminating olive oils on the basis of their geographical origin, in a small area like south Greece. Additionally, the introduced method includes a complete database (as a demonstration tool, mainly for olive oil) in order to be used by any concerned laboratory.