An oil or fat composition described herein has a hydrogenated aroma and flavor as a conventional oil or fat composition and a long lasting hydrogenated aroma, while having trans-fatty acid content reduced to the same extent as that in a general liquid salad oil, and the starting material thereof. The oxidized and partially hydrogenated oil or fat contains C18:2 trans-isomer from 10 to 60 wt. % on the total constituent fatty acid content basis and has peroxide value from 8 to 350 meq/kg. A ratio by weight of the C18:2 trans-isomer content to C18:1 trans-isomer content in all the constituent fatty acids can be 0.3 to 1.8.
