The method according to the invention has the steps of A) providing a feed gas flow a which contains n-butene; B) feeding the n-butene-containing feed gas flow a and an oxygen-containing gas into a dehydrogenation reactor and oxidatively dehydrogenating n-butene into butadiene; C) cooling and compressing the product gas flow b in at least one cooling stage comprising a quench column and in a compression stage comprising a compressor, wherein the product gas flow b is brought into contact with at least one coolant being circulated; D) separating non-condensable and low-boiling gas components as gas flow d2 out of the gas flow c2 by absorbing the C
4 hydrocarbons in at least one absorption agent being circulated; E) separating the C
4 product flow d1 into a material flow e1, which contains butadiene and a selective solvent, and a material flow e2, which contains n-butene, by means of an extractive distillation using the solvent which is selective for butadiene; F) distilling the material flow e1, which contains butadiene and the selective solvent, into a material flow f1, which substantially consists of the selective solvent, and a butadiene-containing material flow f2. The invention is characterized in that the following measures (i) to (iii) are taken: (i) preventing the formation of explosive gas mixtures by monitoring the oxygen concentration in the oxygen-containing gas flows fed into the dehydrogenation zone and controlling the mass flows of oxygen-containing gas flows and hydrocarbon-containing gas flows such that no explosive gas mixtures can be formed; (ii) interrupting the supply of the oxygen-containing gas mixture into the dehydrogenation zone if a threshold for the oxygen concentration in the dehydrogenation gas mixture is exceeded; and (iii) carrying out steps A) to F) in equipment which is designed to be explosion-resistant, wherein liquid-conducting pipelines are designed to be explosion-resistant, and gas lines are designed to be detonation-resistant.