A procedure for the alkylation of isobutane by olefinic hydrocarbons, in which a first hydrocarbon charge (3) rich in isobutane is put in contact with a second hydrocarbon charge rich in light olefins (2), under conditions that will provoke the alkylation of the isobutane by the light olefins, the effluents that emanate from the reaction area in a fractionation column (6) are treated in order to extract therefrom at least a first cut rich in alkylate (7), a second cut rich in normal butane (8) and a third cut rich in isobutane (9), said third cut (9) is then recycled at the entry of the alkylation reaction area. The second cut (8) rich in normal butane is purified (12) so as to lower its content in compounds with 5 or more carbon atoms to a value that is less than or equal to 5% by weight, the cut thus purified (14) is treated in an isomerization reactor (16) of normal butane to isobutane, this cut is then recycled (21) at the entry of the alkylation effluents fractionation column (6).