Preheat oven to 425 degrees F. Grease the bottom and 1/2-inch up the sides of a 9x9x2-inch baking pan; set aside. In a medium mixing bowl stir together flour, cornmeal, sugar, baking powder, and salt. Make a well in the center of the dry mixture; set aside.
In a small mixing bowl combine the eggs, buttermilk, and cooking oil. Add egg mixture all at once to dry mixture. Stir just until moistened. Gently stir in chopped red sweet pepper. Spoon batter into the prepared pan.
Bake for 20 to 25 minutes or until a wooden toothpick inserted near the center comes out clean. Serve warm. Makes 9 servings.