Process for semi-permanent straightening of human hair, characterized in that it provides for the following application steps: a) Application on hair of an aqueous solution containing a buffering agent of the alpha-keto acid family, wherein the buffering agent is glyoxylic acid, which is dissolved at a ratio between 5% and 25% in weight; b) Permanence of the glyoxylic acid in contact with hair for 15 to 120 minutes; c) Hair drying, d) Hair straightening with hair straightening iron at a temperature of 200 ± 50 °C wherein a procedure of the following steps i to x is excluded: i contacting wavy, curly hair with an alkaline composition comprising a sufficient amount of chemical base to provide alkalinity in the range of 8.5 to about pH 14 to partially straighten the original configuration of the hair; ii optionally washing the partially straightened hair with water; iii drying the partially straightened hair to a substantially dry state; iv contacting the so-dried hair with an acidic composition having acidity of less than about pH 1.5, the acidic composition comprising glyoxylic acid in an amount sufficient to further straighten the configuration of the hair, the amount being in the range of 5 to 20 active weight percent, based on the total weight of the finished composition; v covering the so-contacted hair of step iv with a cap and optionally heating the cap-covered hair for a period of up to about 30 minutes; vi removing the cap and drying the further straightened hair to a substantially dried state; vii pressing the substantially dried straightened hair with a heated iron; the iron being a flat iron heated to a platen temperature in the range of 180 to 230°C; viii washing the pressed, straightened hair with water, and optionally contacting the washed hair with a hair conditioning composition comprising an oxidizing agent, and optionally, washing the conditioned hair with water, ix blow drying the hair of step viii optionally with a thermal protectant composition on the hair; and x optionally pressing the blow-dried hair with a heated iron, optionally with a hair conditioning composition on the hair. a) Application on hair of an aqueous solution containing a buffering agent of the alpha-keto acid family, wherein the buffering agent is glyoxylic acid, which is dissolved at a ratio between 5% and 25% in weight; b) Permanence of the glyoxylic acid in contact with hair for 15 to 120 minutes; c) Hair drying, d) Hair straightening with hair straightening iron at a temperature of 200 ± 50 °C i contacting wavy, curly hair with an alkaline composition comprising a sufficient amount of chemical base to provide alkalinity in the range of 8.5 to about pH 14 to partially straighten the original configuration of the hair; ii optionally washing the partially straightened hair with water; iii drying the partially straightened hair to a substantially dry state; iv contacting the so-dried hair with an acidic composition having acidity of less than about pH 1.5, the acidic composition comprising glyoxylic acid in an amount sufficient to further straighten the configuration of the hair, the amount being in the range of 5 to 20 active weight percent, based on the total weight of the finished composition; v covering the so-contacted hair of step iv with a cap and optionally heating the cap-covered hair for a period of up to about 30 minutes; vi removing the cap and drying the further straightened hair to a substantially dried state; vii pressing the substantially dried straightened hair with a heated iron; the iron being a flat iron heated to a platen temperature in the range of 180 to 230°C; viii washing the pressed, straightened hair with water, and optionally contacting the washed hair with a hair conditioning composition comprising an oxidizing agent, and optionally, washing the conditioned hair with water, ix blow drying the hair of step viii optionally with a thermal protectant composition on the hair; and x optionally pressing the blow-dried hair with a heated iron, optionally with a hair conditioning composition on the hair.