An object of the present invention is to clone a gene which is involved in synthesis of fatty acid having trans-11-, cis-13-conjugated double bonds from fatty acid having a double bone at position .DELTA.12. The present invention provides a gene having any one of the following nucleotide sequences: (A) a nucleotide sequence encoding an amino acid sequence shown in SEQ ID NO: 1 or 12; (B) a nucleotide sequence encoding an amino acid sequence comprising a deletion, addition or substitution of one or several amino acids with respect to the amino acid sequence shown in SEQ NO: 1 or 12, and having an ability of synthesizing fatty acid having trans-11-, cis-13-conjugated double bonds from fatty acid having a double bond at position .DELTA.12; (C) a nucleotide sequence shown in SEQ ID NO: 2 or 13; (D) a nucleotide sequence comprising a deletion, addition or substitution of one or several nucleotides with respect to the nucleotide sequence shown in SEQ ID NO: 2 or 13, and encoding a protein having an ability of synthesizing fatty acid having trans-11-, cis-13-conjugated double bonds from fatty acid having a double bond at position .DELTA.12; and (E) a nucleotide sequence hybridizing with the nucleotide sequence shown in SEQ ID NO: 2 or 13 or a complementary sequence thereof under stringent conditions, and encoding a protein having an ability of synthesizing fatty acid having trans-11-, cis-13-conjugated double bonds from fatty acid having a double bond at position .DELTA.12.