A process for preparing butadiene from n-butenes, comprising the steps of: A) providing an input gas stream comprising n-butenes; B) feeding the input gas stream comprising n-butenes and a gas containing at least oxygen into at least one oxidative dehydrogenation zone and oxidatively dehydrogenating n-butenes to butadiene, giving a product gas stream; Ca) cooling the product gas stream by contacting with a circulating cooling medium in at least one cooling zone; Cb) compressing the cooled product gas stream in at least one compression stage, giving at least one aqueous condensate stream c1 and one gas stream c2; D) removing uncondensable and low-boiling gas constituents comprising oxygen and low-boiling hydrocarbons as gas stream d2 from the gas stream c2 by absorbing the C4 hydrocarbons in an absorbent, 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; E) separating the C4 product stream d1 by extractive distillation; F) distilling the stream e1 into a stream f1 consisting essentially of the selective solvent and a stream f2 comprising butadiene; G) removing a portion of the aqueous phase of the cooling medium which circulates in step Ca) as aqueous purge stream g; H) distillatively separating the aqueous purge stream g into a fraction h1 and a fraction h2 depleted of organic constituents.