[Problem] In oxidative hair dyes, there is a tendency that the number of kinds of a first preparation is increasing in order to meet a growing need to highly control the color of hair and, consequently, the number of kinds of a first preparation for already dyed parts of hair is also increasing. As a result, such a problem arises that the consumed amount of a first preparation for each color decreases and the quality of the first preparation is deteriorated during a period after a package of the first preparation is opened and before the first preparation is gone through. In these situations, the present invention addresses the problem of preventing the increase in the number of kinds of a first preparation for already dyed parts of hair.[Solution] In order to solve the problem, an oxidant-containing composition that can be used as a second preparation of a hart treating agent is provided. The oxidant-containing composition is characterized by comprising (A) and acid and (B) an oxidant, wherein the acid (A) is contained in an amount of 0.4% by mass or more. According to the oxidant-containing composition, it is possible to prevent the accumulation of damage to hair even when a first preparation for newly grown parts of hair is used. Therefore, it becomes possible to also use the first preparation for newly grown parts of hair as a first preparation for already dyed parts of hair, resulting in the reduction in the number of kinds of the first preparation.[Problème] Dans les teintures oxydantes pour cheveux, il y a une tendance à augmenter le nombre de sortes d'une première préparation afin de satisfaire un besoin croissant de contrôle précis de la couleur des cheveux et, par conséquent, le nombre de sortes d'une première préparation pour des cheveux déjà colorées est également augmenté. Par conséquent, le problème se pose de la quantité consommée d'une première préparation pour chaque couleur diminue, et la qualité de la première préparation est détériorée pendant
