An aliphatic alkylate with a high octane number is prepared from a C4 catalytic cracking or steam-cracking fraction that contains mainly isobutane, isobutene, butene-1 and butenes-2 by: (a) hydro-isomerizing said C4 fraction, obtaining a mixture that contains for the most part butenes-2, isobutene and isobutane; (b) separating, by distillation of the hydro-isomerized fraction, of a butene-2-rich effluent that is collected at the bottom and an isobutane- and isobutene-rich effluent that is collected at the top; (c) sending said isobutene- and isobutane-rich effluent into a hydrogenation zone that produces an effluent that for the most part contains isobutane; (d) sending of said butenes-2-rich effluent that is derived from (b) and of said effluent that for the most part contains the isobutane that is derived from (c) into an alkylation zone producing, by addition of isobutane to butenes-2, an isooctane mixture that contains excess isobutane; (e) separating by distillation of excess isobutane, which comes out at the top, and alkylate with an improved octane number, which comes out at the bottom; and (f) recycling of the excess isobutane that is recovered in (e) upstream from hydrogenation (c) of the top effluent from the distillation of (b).