A process for preparing butadiene from n-butenes, comprising the steps of: A) providing an input gas stream a1 comprising n-butenes; B) feeding the input gas stream a1 comprising n-butenes, an oxygenous gas and an oxygenous cycle gas stream a2 into at least one oxidative dehydrogenation zone and oxidatively dehydrogenating n-butenes to butadiene, giving a product gas stream b comprising butadiene, unconverted n-butenes, steam, oxygen, low-boiling hydrocarbons and high-boiling secondary components, with or without carbon oxides and with or without inert gases; Ca) cooling the product gas stream b and optionally at least partly removing high-boiling secondary components and steam, giving a product gas stream b'; Cb) compressing and cooling the product gas stream b' in at least one compression and cooling stage, giving at least one aqueous condensate stream c1 and one gas stream c2 comprising butadiene, n-butenes, steam, oxygen and low-boiling hydrocarbons, with or without carbon oxides and with or without inert gases; Da) absorbing the C4 hydrocarbons comprising butadiene and n-butenes in an aromatic hydrocarbon solvent as an absorbent and removing uncondensable and low-boiling gas constituents comprising oxygen, low-boiling hydrocarbons, any carbon oxides, aromatic hydrocarbon solvent and any inert gases as gas stream d2 from the gas stream c2, giving an absorbent stream laden with C4 hydrocarbons and the gas stream d2, and then desorbing the C4 hydrocarbons from the laden absorbent stream, giving a C4 product gas stream d1; Db) at least partly recycling the gas stream d2 as cycle gas stream a2 into the oxidative dehydrogenation zone, wherein the content of aromatic hydrocarbon solvent in the cycle gas stream a2 is limited to less than 1% by volume.