Abstract: A process for making a bio-diesel and a bio-naphtha from a complex mixture of natural occurring fats & oils may include subjecting the complex mixture to a refining treatment for removing non-triglyceride and non-fatty acid components, thereby obtaining refined oils. The complex mixture or refined oils may be subjected hydrolysis for obtaining glycerol and free fatty acids. The free fatty acids may be subjected to fractionation for obtaining: a liquid part (phase L); and a solid part (phase S). The phase L may be transformed into alkyl-esters as bio-diesel by an esterification. The phase S may be transformed into linear paraffins as the bio-naphtha by: hydrodeoxygenation or decarboxylation of the free fatty acids; or obtaining fatty acids soaps from the phase S and decarboxylation of the fatty acids soaps.