The present invention relates to a composition for reshaping keratin fibers, preferably the hair, having a specific range of a pH and including at least one specific active compound in an amount of 8% by weight or more relative to the total weight of the composition. The composition according to the present invention is preferably a cosmetic composition, for keratin fibers, such as hair, and can be used for a process for reshaping the keratin fibers with heat. The process according to the present invention can be used to deform or reshape keratin fibers, preferably hair, and can provide the keratin fibers with sufficient reshaping efficiency such as strong wave intensity of the curled keratin fibers and excellent hair conditioning effects (less damage to the keratin fibers), in a relatively short period of time as compared to a conventional process which uses a reducing agent and an oxidizing agent.