In a bowl stir together the flour, the cornmeal, the baking powder, and the salt. In a small bowl whisk together the milk, the egg, and the butter, and stir the mixture into the cornmeal mixture, stirring until the batter is just combined. Pour the batter into a greased 8-inch-square baking pan and bake the corn bread in the middle of a preheated 425°F oven for 20 to 25 minutes, or until the top is pale golden and a tester comes out clean. Let the corn bread cool in the pan for 5 minutes, invert it onto a rack, and let it cool completely.