Present invention relates to a process for permanent shaping of human hair used both for the permanent waving of human hair with an excellent waving effect as well as for the straightening of curled hair. Present invention is a process for permanent shaping hair wherein hair is optionally washed or wetted or shampooed and a composition comprising at least one reducing agent is applied and rinsed off from hair after a processing time of 1 to 30 min and at a temperature of 20 to 45° C. and a composition comprising at least one oxidizing agent is applied and processed for 1 to 20 min at a temperature range of 20 to 45° C. and rinsed off from hair wherein at least one of the two compositions comprise a thickening polyurethane polymer.