A process for preparing C5/C6-olefins from an olefinic starting stream comprising C4-hydrocarbons comprises a) carrying out a metathesis reaction in the presence of a metathesis catalyst so as to convert the 1-butene, 2-butene and isobutene present in the starting stream into a mixture of C2-C6-olefins and butanes, b) firstly fractioning the resulting product stream by distillation to give a low boiler fraction A comprising C2-C4-olefins and butanes or C2-C3-olefins, which is discharged, and a high boiler fraction comprising C4-C8-olefins and butanes, c) fractioning the high boiler fraction from b) by distillation to give a low boiler fraction B comprising butenes and butanes, an intermediate boiler fraction C comprising pentene and methylbutene and a high boiler fraction D comprising hexane and methylpentene, d) where all or part of the fraction B and/or C are recirculated to the process step a) and the fraction D is discharged as product.