Hair straightening method comprising: - a stage of application on the hair of a straightening composition containing at least one alpha-hydroxy acid derivative, the pH of this composition being less than or equal to 7, - then a step for raising the temperature of the hair, with the help of a heating medium, at a temperature between 140 and 250 ° C, by applying a plate made in continuous movement from the root to the tip, in one or several steps, being the derizing procedure performed without reduction or lantionization step, the alpha hydroxy acid derivative being selected from the compounds of formula (I): ** Formula ** R1>； = H, OH, NH2, CH2-COOH, C1- alkyl Linear or branched C4 R2>； = H, COOH, CHOH-COOH, CF3, CH>； = CH2, NHCONH2, linear or branched or cyclic C1-C8 alkyl, optionally substituted with a radical selected from OH, Cl, NH2, COOH, CF3 or SCH3； phenyl or benzyl optionally substituted with 1 OH or OCH3 radical； ** Formula ** or also the radical R1 and R2 can also together form an oxo radical (>； = O) or a cyclopropyl or cyclobutyl or hydroxycyclobutyl ring or ** Formula ** cyclopentyl or cyclohexyl with the carbon atom that carries them or also a radical when R1>； = H, R2 can also represent the radical (CHOH) 2CH2OH or (CHOH) 3CH2OH R>； = OH or NR3R4 with R3, R4>； = H or linear or branched C1-C4 alkyl optionally substituted with 1 or 2 OH radicals and their stereoisomers and organic or mineral salts and solvates.Procedimiento de desrizado del cabello que comprende: - una etapa de aplicación sobre el cabello de una composición de desrizado que contiene al menos un derivado de alfa-hidroxi-ácido, siendo el pH de esta composición inferior o igual a 7, - después una etapa de elevación de la temperatura del cabello, con la ayuda de un medio de calentamiento, a una temperatura comprendida entre 140 y 250ºC, por aplicación de una plancha hecha en movimiento continuo desde la raíz hasta la punta, en uno o varios pasos, siendo el procedimiento de des
