The present invention relates to a new process for obtaining fatty acids with improved color, odor and heat stability which is characterized in that: (a) in a first step the crude acids are fed to a rectification (“precut”) column in order to remove low boiling by-products being present in the starting material as a top fraction, and (b) in a second step the bottom fraction of the precut column is fed to a sidestream column in order to obtain the pure fatty acids as the side fraction, to remove low boiling by-products which have been formed in the course of the first distillation as a top fraction and to remove high boiling by-products, either being present from the starting material or formed during the first distillation, with the residue.