The invention relates to a composition comprising, in a physiologically acceptable aqueous medium, a dicarboxylic acid containing from 2 to 8 carbon atoms, and a plant oil of triglyceride type with a fatty acid fraction comprising not more than 20% by weight of oleic acid, the composition having a pH ranging from 7 to 11. Process for straightening African-type hair using the composition and a straightening step with an iron at a temperature of at least 100° C.
