The invention relates to a method, according to which C4-C6 olefins or an olefin fraction which is essentially free of sulphur and contains C4-C6 olefins are isomerised on a contact containing an element of the eighth subgroup of the periodic table of elements, in the presence of at least one added sulphur compound, and the polyunsaturated hydrocarbons which are optionally contained therein are selectively subjected to hydrogenation and hydroisomerisation. The sulphur compounds are separated from the product and are optionally redirected into the educt in order to create products which are practically free of sulphur.