A process and composition for the aftertreatment of permanently deformed hair. Often the permanent deformation leaves reducing agent or oxidant in the hair, which leads to considerable damage to the hair. Applying to the hair a composition containing glyoxylic acid and at least one organic compound having a multiple carbon-carbon bond, containing a carboxyl group bonded to the multiple bond directly or through a methylene group, which is activated by at least one multiple CO or CN bond conjugated to that multiple bond, avoids the damage caused by permanent deformation.