Disclosed is a method whereby, in producing a hard butter composition being rich in SUS (2-unsaturated-1,3-disaturated triglyceride) via ester exchange by a 1,3-specific lipase, the production can be more conveniently or more efficiently carried out. In producing a hard butter composition being rich in SUS (2-unsaturated-1,3-disaturated triglyceride) via ester exchange by a 1,3-specific lipase, a low-melting point fraction of allanblackia fat is used as the main starting material, saturated fatty acids are selectively introduced into the 1- and 3-positions of the fat, and then fractionation is optionally conducted to thereby give an SUS-rich fraction.