NOVELTY - Production of propylene and coproduction of a desulfurized gasoline of high octane index made of a charge having 4-5 carbon atom fraction (I) resulting from a steam-cracking unit and a fluid catalytic cracked gasoline (FCC) unit comprises selective hydrogenation of the FCC to give an effluent that is sent into a separation unit (21) to give a light fraction sent into an oligocracking unit (40), and a heavy fraction sent into a water-treatment unit (30) and separating the obtained fractions in a distillation columns (50) in to at least 5 fractions e.g. a propylene fraction.    USE - The process is useful to prepare propylene and a desulfurized gasoline (claimed).    ADVANTAGE - The process: provides high octane index gasoline; and is selective (claimed), simple and cost effective. The process also provides high propylene yield.    DETAILED DESCRIPTION - Production of propylene and coproduction of a desulfurized gasoline of high-octane index made of a charge containing 4-5 carbon atom fraction (I) resulting from a steam-cracking unit (A) and a fluid catalytic cracked gasoline (FCC) unit. The process comprises selective hydrogenation of FCC producing an effluent, which is sent into a separation unit (21) to give a light fraction sent into an oligocracking unit (40), and a heavy fraction containing more than 6 carbon atoms is sent into a water-treatment unit (30) and separating the obtained fractions in a distillation columns (50) into at least 5 fractions like: a fraction mainly made up of ethylene; a fraction of propylene; an intermediate fraction having a 4 carbon molecule in which a part is recycled at the entry of the oligocracking unit, and a non-recycled part is upgraded in liquefied petroleum gas; an intermediate fraction mainly made up of 5-6 carbon atom molecule in which a part is recycled at the entry of the oligocracking unit; and a non recycled part having gasoline directed towards the gasoline pool and a basic fraction of 9 carbon atom molecule sent in to the water-treatment unit in which an effluent from the water-treatment unit having the desulfurized gasoline.    DESCRIPTION OF DRAWING(S) - The figure shows an outline of the process:    Separation unit (21)    Water-treatment unit (30)    Oligocracking unit (40)    Distillation columns (50)    Aromatic extraction unit (60)