Hair dye compositions comprise (A) ammonia or an ammonium salt, (B) a carbonate (other than an ammonium salt), (C) a transition metal salt, and (D) a chelating agent, and have a pH of from 8.5 to 12. They do not give off an intensely irritating odor and have low irritating property, can change hair into a lighter tone in a short time or can dye hair well in a color ranging from a light color to a deep color, and moreover, assure good retention of the thus-obtained tone or color.