The present invention relates to a process for smoothing / hair straightening of the hair, which comprises (i) the application on the hair, of a cosmetic composition comprising at least of glyoxylic acid and / or at least one of its derivatives, the composition having a ph of less than or equal to 4, (ii) an exposure time of the composition with glyoxylic acid and / or one of its derivatives, of at least 10 minutes, followed by (iii) the application without rinsing of a composition comprising at least one compound of the treatment of hair chosen from fatty alcohols and the conditioners cationic, and (iv) of a phase of application of heat, comprising at least one step of heating at a temperature of at least 150°C. the smoothing of the hair, according to the invention is effective in terms of the smoothing and rapid to use.
