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, low-boiling secondary constituents, hydrogen 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) introduction of the C4 product gas stream c consisting essentially of n-butane, 1-butene, 2-butene and butadiene into a selective hydrogenation zone and selective hydrogenation of butadiene to 1- and/or 2-butene to give a stream d consisting essentially of n-butane, 1-butene and 2-butene; E) separation of the stream d into a desired product stream e1 consisting essentially of 1-butene and a recycle stream e2 consisting essentially of 2-butene and n