PURPOSE: To obtain the titled compound useful as a surface active agent efficiently, industrially and advantageously, by oxidizing an alkyl tertiary amine containing a branched-chain alkyl tertiary amine with hydrogen peroxide in the presence of inexpensively and readily obtainable sodium pyrophosphate.

CONSTITUTION: An alkyl tertiary amine (e.g. alkyl tertiary amine containing 10W20 total carbons, etc.) containing a branched-chain tertiary amine [compound shown by the formula (R1 and R2 are methyl or ethyl; R3 and R4 are ≥1C straight-chain alkyl, R3+R4=6W16C)] is oxidized with hydrogen peroxide in the presence of sodium pyrophosphate to give an amine oxide. Sodium pyrophosphate decahydrate is readily obtainable so preferably used as the sodi um pyrophosphate. The amount of sodium pyrophosphate added is preferably 0.02W2wt.% calculated as anhydrous sodium pyrophosphate based on the tertiary amine. The reaction is ordinarily carried out in water solvent at 50W80°C.