The present invention relates to a method for semipermanent straightening and bleaching of the hair in two steps, which are carried out one after another in one salon visit. For this purpose, the method of the present invention uses a first composition (straightening composition) comprising at least one carboxylic acid of the Formula (I) and a second composition, (bleaching composition) comprising least one oxidizing agent and at least one alkalizing agent. The hair is treated with the said compositions successively, so that the bleaching treatment is performed directly after the straightening treatment.