The subject matter of the present invention is a method for straightening/relaxing the hair, which comprises (i) the application to the hair of a cosmetic composition comprising at least glyoxylic acid and/or at least one derivative thereof, the composition having a pH of less than or equal to 4, (ii) a leave on time for the composition comprising glyoxylic acid and/or at least one derivative thereof of at least 10 min, followed by (iii) the application, without rinsing, of a composition comprising at least one hair treatment compound chosen from fatty alcohols and cationic conditioning agents, and then by (iv) a heat application step comprising at least one step of heating at a temperature of at least 150° C.The method for straightening the hair according to the invention is effective in terms of straightening and quickly implemented.
