The method comprises separation of contacting products into liquid and gaseous products, complete burning of gaseous products in the presence of the catalyst of complete oxidation of light hydrocarbons and addition of carbon dioxide and water vapor mixture formed during burning to the raw paraffin hydrocarbons. The mixture of paraffin hydrocarbons C.sub.2/C.sub.5 is used as a raw material in this method. Before feeding the said mixture of hydrocarbons the catalyst is subjected to treatment by paraffin hydrocarbons C.sub.3/C.sub.4 mixed with mercaptan so that the amount of mercaptan passed through the catalyst is 0.01 0.1 mass % of the catalyst weight.