Provided is a hair dye composition to be used as a mixture of a first part containing an alkali agent and a second part containing an oxidizing agent, wherein the composition comprises (a) a triazacyclononane compound (1) or salt thereof, (b) 0.1 to 12 wt. %, in terms of hydrogen peroxide, of an oxidizing agent, and (c) 0.05 to 10 wt. % of an alkali agent, and the mixture has a pH of from 7.5 to 12. ##STR00001## (R.sup.1 to R.sup.4: H or C.sub.1-6 alkyl which may be substituted by OH, R.sup.5 to R.sup.7: H, (substituted) C.sub.1-6 alkyl, (substituted) aralkyl, (substituted) heteroarylalkyl, (substituted) aryl, (substituted) heteroaryl, (substituted) C.sub.1-6 acyl, or a group (2) (in which R.sup.8 to R.sup.12 represents H, C.sub.1-6 alkyl, aralkyl or aryl and n stands for 2 to 30).The hair dye composition of the present invention has excellent hair bleaching power, can dye the hair into a bright favorable color tone, and moreover has less hair damage and less scalp irritation.