Auxiliary enzyme of beta-oxidation. It participates in the metabolism of unsaturated fatty enoyl-CoA esters having double bonds in both even- and odd-numbered positions. Catalyzes the NADP-dependent reduction of 2,4-dienoyl-CoA to yield trans-3-enoyl-CoA. a (2E,4E)-dienoyl-CoA + H(+) + NADPH = a 4,5-saturated-(3E)-enoyl-CoA + NADP(+) a (2E,4Z)-dienoyl-CoA + H(+) + NADPH = a 4,5-saturated-(3E)-enoyl-CoA + NADP(+) Belongs to the short-chain dehydrogenases/reductases (SDR) family. 2,4-dienoyl-CoA reductase subfamily.