A process for making 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 non-triglyceride and non-fatty acid components, thereby obtaining refined fats & oils; said refined fats & oils are transformed into linear or substantially linear paraffin's as the bio-naphtha by an hydrodeoxygenation or from said refined fats & oils 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 refined fats & oils are obtained fatty acids soaps that are transformed into linear or substantially linear paraffin's as the bio-naphtha by decarboxylation of the soaps.