A process for preparing butadiene from n-butenes, comprising the steps of: absorbing C4 hydrocarbons comprising butadiene and n-butenes, obtained from oxidative dehydrogenation of 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, 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; and 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.