A method for manufacturing a fatty acid derivative represented by formula: wherein X 1 is Y 1 is Z 1 is wherein R1, R2 and R3 is a protecting group for hydroxy group independently selected from the group including methyl, methoxymethyl, ethyl, 1-ethoxyethyl, benzyl, substituted benzyl, allyl, tetrapyranyl, t-butyldimethylsilyl, triethylsilyl, triisopropylsilyl, diphenylmethylsilyl, formyl, acetyl, substituted acetyl, benzoyl, substituted benzoyl, methyloxycarbonyl, benzyloxycarbonyl, t-buthloxycarbonyl and allyloxycarbonyl groups, provided that at least one of X 1, Y 1 and Z 1 is A is -CH 3, -CH 2 OH, -COCH 2 OH, -COOH or a salt, ether, ester, or amide thereof; B is a single bond, -CH 2 -, -CH 2 -CH 2 -, -CH=CH- or -C≡C-, -CH 2 -CH 2 -CH 2 -, -CH=CH-CH 2 -, -CH 2 -CH=CH-, -C≡C-CH 2 - or -CH 2 -C ≡C-; Ra is bivalent saturated or unsaturated C1-C14 aliphatic hydrocarbon group, which is unsubstituted or substituted by halogen atom, C1-C6 alkyl, C1-C6 alkoxy, oxo, aryl or heterocyclic group, provided that one or more carbon atoms of the aliphatic hydrocarbon group may optionally be replaced with oxygen, nitrogen or sulfur atom; and Rb is hydrogen atom; saturated or unsaturated C1-C14 aliphatic hydrocarbon group which is unsubstituted or substituted by a halogen, oxo, hydroxy, C1-C6 alkoxy, C1-C6 alkanoyloxy, cyclo(C3-C6)alkyl, cyclo(C3-C6)alkyloxy, aryl, aryloxy, heterocyclic or heterocyclic oxy; cyclo(C3-C6)alkyl; cyclo(C3-C6)alkyloxy; aryl; aryloxy; heterocyclic; or heterocyclic oxy, which comprises the step of, reacting a compound of formula: wherein, X 2 is the same as X 1 except for when X 1 is X 2 is Y 2 is the same as Y 1 except for when Y 1 is Y 2 is or Z 2 is the same as Z 1 except for when Z 1 is Z 2 is or provided that at least one of X 2, Y 2 and Z 2 is and, A, B, Ra and Rb are the same as above; with a co-oxidizer under the presence of an azaadamantane-N-oxyl derivative. wherein X 1 is Y 1 is Z 1 is wherein R1, R2 and R3 is a protecting group for hydroxy group independently selected from the group including methyl, methoxymethyl, ethyl, 1-ethoxyethyl, benzyl, substituted benzyl, allyl, tetrapyranyl, t-butyldimethylsilyl, triethylsilyl, triisopropylsilyl, diphenylmethylsilyl, formyl, acetyl, substituted acetyl, benzoyl, substituted benzoyl, methyloxycarbonyl, benzyloxycarbonyl, t-buthloxycarbonyl and allyloxycarbonyl groups, provided that at least one of X 1, Y 1 and Z 1 is A is -CH 3, -CH 2 OH, -COCH 2 OH, -COOH or a salt, ether, ester, or amide thereof; B is a single bond, -CH 2 -, -CH 2 -CH 2 -, -CH=CH- or -C≡C-, -CH 2 -CH 2 -CH 2 -, -CH=CH-CH 2 -, -CH 2 -CH=CH-, -C≡C-CH 2 - or -CH 2 -C ≡C-; Ra is bivalent saturated or unsaturated C1-C14 aliphatic hydrocarbon group, which is unsubstituted or substituted by halogen atom, C1-C6 alkyl, C1-C6 alkoxy, oxo, aryl or heterocyclic group, provided that one or more carbon atoms of the aliphatic hydrocarbon group may optionally be replaced with oxygen, nitrogen or sulfur atom; and Rb is hydrogen atom; saturated or unsaturated C1-C14 aliphatic hydrocarbon group which is unsubstituted or substituted by a halogen, oxo, hydroxy, C1-C6 alkoxy, C1-C6 alkanoyloxy, cyclo(C3-C6)alkyl, cyclo(C3-C6)alkyloxy, aryl, aryloxy, heterocyclic or heterocyclic oxy; cyclo(C3-C6)alkyl; cyclo(C3-C6)alkyloxy; aryl; aryloxy; heterocyclic; or heterocyclic oxy, wherein, X 2 is the same as X 1 except for when X 1 is X 2 is Y 2 is the same as Y 1 except for when Y 1 is Y 2 is or Z 2 is the same as Z 1 except for when Z 1 is Z 2 is or provided that at least one of X 2, Y 2 and Z 2 is and, A, B, Ra and Rb are the same as above;