The present invention relates to a process for treating keratin fibres, in particular the hair, comprising: a) the application, to said fibres, of a composition having a pH greater than or equal to 8, at 25°C, and comprising at least one amino acid chosen from those of formulae (I) and (II) below, and also the betaine forms thereof, the optical isomers thereof, the solvates thereof such as the hydrates, and the organic or inorganic base or acid salts thereof: in which formulae (I) and (II): -R represents a hydrogen atom, or a linear or branched, preferably linear, C1-C5 alkyl group, said alkyl group being optionally substituted with at least one group chosen from hydroxyl, -C(O)-OH, -S(O)2-OH, -C(O)-O-, M+, and -S(O)2-O-, M+, with M+ representing a cationic counterion such as an alkali metal, alkaline-earth metal, or ammonium,20 -n is 0 or 1； b) followed by a step of straightening/relaxing the keratin fibres by means of a straightening iron at a temperature of at least 100°C.
