alternately reducing and oxidizing a working solution containing anthraquinone compounds as a reaction medium, wherein a mixture of alkyl-substituted anthraquinones and alkyl-substituted tetrahydroanthraquinones in a molar ratio of from 2:1 to 8:1 is used as the anthraquinone compounds in the working solution, in said reduction step all of the tetrahydroanthraquinones and some or all of the anthraquinones in the working solution are reduced; and keeping the content of alkyl-substituted anthrahydroquinones in the working solution after said reduction step and before said oxidation step higher than the content of alkyl-substituted tetrahydroanthrahydroquinones, wherein ethylanthraquinone and ethyltetrahydroanthraquinone are used as anthraquinone compounds in the working solution in a total proportion of both of from 10 to 45 mol % of all of the anthraquinone compounds in the working solution.