A method for separating a hydrocarbon mixture, which is obtained at least in part by steam cracking and which contains at least hydrocarbons having one, two and three carbon atoms, including ethane and ethylene, a first fraction initially being obtained from the hydrocarbon mixture by separating off other components at least in part, said fraction containing the predominant part of the hydrocarbons having two or more carbon atoms previously contained in the hydrocarbon mixture or the predominant part of the hydrocarbons having two or fewer carbon atoms previously contained in the hydrocarbon mixture, further fractions subsequently being obtained from the first fraction. A fraction containing ethane is separated off in an amount which reduces the ethane content in the first fraction to less than 25%, the fraction containing ethane being low in or free from other hydrocarbons having two carbon atoms.