Abstract: A) Provision of an n-butane-containing feed gas stream a; B) introduction of the n-butane-containing feed gas stream a into at least one dehydrogenation zone and nonoxidative catalytic dehydrogenation of n-butane to give a product gas stream b comprising n-butane, 1-butene, 2-butene, butadiene, hydrogen, low-boiling secondary constituents and possibly water vapor; C) removal of hydrogen, the low-boiling secondary constituents and, if appropriate, water vapor to give a C4 product gas stream c consisting essentially of n-butane, 1-butene, 2-butene and butadiene; D) separation of the C4 product gas stream c into a recycle stream d1 consisting essentially of n-butane and a stream d2 comprising 1-butene, 2-butene and butadiene by extractive distillation and recirculation of the recycle stream d1 consisting essentially of n-butane to the dehydrogenation zone; E) introduction of the stream d2 comprising 1-butene, 2-butene and butadiene into a selective hydrogenation zone and selective hydrogenation of butadiene to