A process for preparing butadiene from n-butenes, comprising the steps of: A) providing an input gas stream a comprising n-butenes; B) feeding the input gas stream a 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 b comprising butadiene, unconverted n-butenes, water vapor, 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 by contacting with a circulating cooling medium in at least one cooling zone, the cooling medium being at least partly recycled and having an aqueous phase and an organic phase comprising an organic solvent, wherein the solvent used in step Ca) is selected from toluene, o-, m- and p-xylene, mesitylene, mono-, di- and triethylbenzene, mono-, di- and triisopropylbenzene and mixtures thereof; Cb) compressing the cooled product gas stream b which may have been depleted of high-boiling secondary components in at least one compression stage, giving at least one aqueous condensate stream c1 and one gas stream c2 comprising butadiene, n-butenes, water vapor, oxygen and low-boiling hydrocarbons, with or without carbon oxides and with or without inert gases; D) removing uncondensable and low-boiling gas constituents comprising oxygen and low-boiling hydrocarbons, with or without carbon oxides and with or without inert gases, as gas stream d2 from the gas stream c2 by absorbing the C 4 hydrocarbons comprising butadiene and n-butenes in an absorbent, giving an absorbent stream laden with C 4 hydrocarbons and the gas stream d2, and then desorbing the C 4 hydrocarbons from the laden absorbent stream, giving a C 4 product gas stream d1; E) separating the C4 product stream d1 by extractive distillation with a butadiene-selective solvent into a stream e1 comprising butadiene and the selective solvent and a stream e2 comprising n-butenes; F) distilling the stream e1 comprising butadiene and the selective solvent into a stream f1 consisting essentially of the selective solvent and a stream f2 comprising butadiene; which comprises G) removing a portion of the aqueous phase of the cooling medium which circulates in step Ca) and has an aqueous phase and an organic phase as aqueous purge stream g; H) distillatively separating the aqueous purge stream g into a fraction h1 enriched in organic constituents and a fraction h2 depleted of organic constituents; I) at least one fraction i1 is obtained as product of value from the stream h1. A) providing an input gas stream a comprising n-butenes; B) feeding the input gas stream a 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 b comprising butadiene, unconverted n-butenes, water vapor, 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 by contacting with a circulating cooling medium in at least one cooling zone, the cooling medium being at least partly recycled and having an aqueous phase and an organic phase comprising an organic solvent, wherein the solvent used in step Ca) is selected from toluene, o-, m- and p-xylene, mesitylene, mono-, di- and triethylbenzene, mono-, di- and triisopropylbenzene and mixtures thereof; Cb) compressing the cooled product gas stream b which may have been depleted of high-boiling secondary components in at least one compression stage, giving at least one aqueous condensate stream c1 and one gas stream c2 comprising butadiene, n-butenes, water vapor, oxygen and low-boiling hydrocarbons, with or without carbon oxides and with or without inert gases; D) removing uncondensable and low-boiling gas constituents comprising oxygen and low-boiling hydrocarbons, with or without carbon oxides and with or without inert gases, as gas stream d2 from the gas stream c2 by absorbing the C 4 hydrocarbons comprising butadiene and n-butenes in an absorbent, giving an absorbent stream laden with C 4 hydrocarbons and the gas stream d2, and then desorbing the C 4 hydrocarbons from the laden absorbent stream, giving a C 4 product gas stream d1; E) separating the C4 product stream d1 by extractive distillation with a butadiene-selective solvent into a stream e1 comprising butadiene and the selective solvent and a stream e2 comprising n-butenes; F) distilling the stream e1 comprising butadiene and the selective solvent 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) and has an aqueous phase and an organic phase as aqueous purge stream g; H) distillatively separating the aqueous purge stream g into a fraction h1 enriched in organic constituents and a fraction h2 depleted of organic constituents; I) at least one fraction i1 is obtained as product of value from the stream h1.