NOVELTY - Making bio-diesel, bio-naphtha and optionally bio-propane from a complex mixture of naturally occurring fats and oils, comprises: subjecting complex mixture to refining treatment to remove major part of non-triglyceride and non-fatty acid components to obtain refined oils; subjecting refined oils to fractionation step to obtain liquid triglyceride part (phase-L) and solid triglyceride part (phase-S); transforming phase-L into alkyl-esters as bio-diesel by transesterification; and transforming phase-S into linear or substantially linear paraffin's as the bio-naphtha by an hydro-deoxygenation.    USE - The method is useful for making a bio-diesel, bio-naphtha and optionally bio-propane from a complex mixture of natural occurring fats and oils, where the bio-naphtha is useful as a direct feedstock of a steam cracker to obtain cracked products including bio-ethylene, bio-propylene, bio-butadiene, bioisoprene, bio-(di)cyclopentadiene, bio-piperylenes, bio-benzene, bio-toluene, bio-xylene and bio-gasoline (all claimed).    ADVANTAGE - The method reduces the negative effect due to the production of carbon monoxide and carbon dioxide and traces of low molecular weight oxygenates (aldehydes and acids) in the steam cracker.    DETAILED DESCRIPTION - Making a bio-diesel, a bionaphtha and optionally bio-propane from a complex mixture of naturally occurring fats and oils, comprises: subjecting the complex mixture to a refining treatment for removing the major part of the non-triglyceride and non-fatty acid components, to obtain refined oils; subjecting the refined oils 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); transforming the phase-L into alkyl-esters as biodiesel by transesterification; transforming the phase-S into linear or substantially linear paraffin's as the bio-naphtha by an hydro-deoxygenation, or transforming the phase-S obtained fatty acids into linear or substantially linear paraffin's as the bio-naphtha by hydrodeoxygenation or decarboxylation of the free fatty acids, or transforming the phase-S obtained fatty acids soaps into linear or substantially linear paraffin's as the bio-naphtha by decarboxylation of the soaps. INDEPENDENT CLAIMS are also included for use of bio-naphtha as a direct feedstock of a steam cracker (or in steam cracking process) in order to obtain cracked products including bio-ethylene, bio-propylene, bio-butadiene, bio-isoprene, bio-cyclopentadiene, bio-piperylenes, bio-benzene, biotoluene, bio-xylene and bio-gasoline, or to obtain a ethylene to methane weight ratio of at least 3, resulting from the cracking of bio-naphtha, where the bio-naphtha is used as such, or optionally together with bio-propane, or as blended with at least a conventional feedstock of LPG, naphtha or gas oil.