The present invention relates to a process for the selective production of olefins from light hydrocarbons comprising: a) fractionating a butane fraction in a de-isobutanizer to obtain an enriched iso-butane fraction and an enriched normal-butane fraction, b) cracking said normal-butane fraction and optionally an ethane fraction, optionally a propane fraction, in a non-catalytic cracking zone to produce an olefin rich stream, preferably the ethane fraction, if any, the propane fraction, if any, and normal-butane fractions are cracked in separate non-catalytic cracking zones, c) treating said olefin rich stream in a separating section comprising: removing hydrogen and methane, recovering an ethylene stream, recovering an ethane stream and recycling said stream to the cracking zone, recovering a propylene stream, recovering a propane stream, optionally recycling said stream to the cracking zone, recovering a C4 stream, removing the heavies, d) selectively hydrogenating the dienes and alkynes in the C4 stream produced in step c) into their corresponding olefins, e) reacting by metathesis in a metathesis section the C4 stream produced in step d) and a part of the ethylene stream produced in step c) to produce propylene, f) treating the effluent of step e) to recover: an ethylene stream optionally recycled to the metathesis section, a propylene stream, a C4 and heavies stream, g) optionally treating the C4 and heavies stream produced in step f) which is either hydrogenated, or not-hydrogenated and recycled to the cracking zone optionally through a de-isobutanizer, or recycled directly to the cracking zone, h) optionally transforming the recovered iso-butane of step a) in iso-butene and subsequently transforming the obtained iso-butene in poly-iso-butene, di-iso-butene, alkylate for gasoline blending, t-butyl-ethers, methyl-metacrylate or either reacted with formaldehyde to make isoprene. In an embodiment of the invention a normal-butane fraction and an ethane fraction are cracked in the non-catalytic cracking zone.In another embodiment of the invention a light hydrocarbon feedstock comprising essentially ethane, propane and butane is fractionated to obtain a C3 fraction used as LPG, an ethane fraction and a butane fraction. The butane fraction is sent to the cracking zone through the de-isobutanizer, the ethane fraction is sent to the cracking zone.