Process for making a bio-diesel and a bio-naphtha and optionally bio-propane from a complex mixture of natural occurring fats & oils, wherein said complex mixture is subjected to a refining treatment for removing the major part of the non-triglyceride and non-fatty acid components, thereby obtaining refined oils; said refined oils are subjected to a fractionation step for obtaining: an unsaturated or substantially unsaturated, liquid or substantially liquid triglyceride part (phase L); and a saturated or substantially saturated, solid or substantially solid triglyceride part (phase S); and said phase L is transformed into alkyl-esters as bio-diesel by a transesterification; said phase S is transformed into linear or substantially linear paraffin's as the bio-naphtha: by an hydrodeoxygenation or from said phase S are obtained fatty acids that are transformed into linear or substantially linear paraffin's as the bio-naphtha by hydrodeoxygenation or decarboxylation of the free fatty acids or from said phase S are obtained fatty acids soaps that are transformed into linear or substantially linear paraffin's as the bio-naphtha by decarboxylation of the soaps.