The present invention relates to a process for purifying ethylenediamine, in which a) a mixture comprising water (H2O), ethylenediamine (EDA) and N-methylethylenediamine (NMEDA) is introduced into a rectification column (NMEDA removal column), where the mixture introduced comprises at least the amount of water as required for the formation of a high-boiling azeotrope of EDA and water at the appropriate bottom temperature; and the EDA-comprising bottom product from the NMEDA removal column is introduced into a second rectification column (EDA dewatering column), wherein the pressure at the top of the EDA dewatering column is adjusted such that the boiling temperature of the mixture obtained at the top is 10° C. or higher than the bottom temperature of the NMEDA removal column, which comprises (i) partly or fully condensing the vapors from the top of the EDA dewatering column in a condenser which is cooled with a medium which is at least partly evaporated during the condensation and the vapor thus formed is used at least partly to heat the evaporator of the NMEDA removal column; and/or (ii) introducing the vapors from the top of the EDA dewatering column into the NMEDA removal column.