An improved process and composition for straightening or waving hair is achieved combining ammonium bisulfite and ethanolamine sulfite in a single mixture which is maintained at a pH of between about 6.5 and 8.0. By employing the present invention, long lasting, waved or straightened hair is attained. Furthermore, using the hair waving/straightening composition and method of the present invention, the desired waving and/or straightening of hair fiber is achieved in a single step, without the need for a separate application of an oxidizing or neutralizing agent.