PURPOSE: To obtain the the titled compound useful as a compounding agent for detergents in a short time in high conversion, by reacting a branched chain tertiary amine with an excess amount of hydrogen peroxide, reacting a straight- chain tertiary amine with hydrogen peroxide.

CONSTITUTION: An aliphatic tertiary amine comprising a branched chain alkyl tertiary amine shown by the formula I (R1 and R2 are methyl or ethyl; R4 and R5 are straight-chain alkyl, R4 and R5 have 6W16C in total) as a main component is oxidized with hydrogen peroxide in the presence of preferably an amine oxide. Then, a straight-chain alkyl tertiary amine shown by the formula II(R3 is 6W18C straight-chain alkyl) substantially containing no branched chain alkyl group is added to it, and reacted with hydrogen peroxide to give the desired substance. Instead of addition of the amine oxide, 15W30wt% straight-chain alkyl tertiary amine may be added to the branched chain alkyl tertiary amine.