The i-butene present in a C.sub.4 raffinate I is subjected in a first step to a first hydroisomerization. The hydroisomerization product is subjected to fractional distillation, with essentially 2-butene and n-butane being obtained as bottom product and i-butene and i-butane being obtained as overhead product. The overhead product is condensed and the condensate is divided into two parts. One part is subjected to a second hydroisomerization and the second hydroisomerate is recycled to the upper third of the fractionation column. The other part of the condensed overhead product is fed to the oligomerization. The condensed overhead-product of the fractionation column is divided in such a manner that, based on 1 part by volume of condensate conducted to the oligomerization, 1-5 parts by volume are fed to the second hydroisomerization.