Preheat oven to 375°F Grease and flour a 2 quart rectangular baking dish and set aside. In a medium bowl, combine flour, cornmeal, sugar, baking powder, and salt.
In a large mixing bowl, beat butter with an electric mixer for 30 seconds. Add eggs one at a time, beating well after each addition. Beat in flour/cornmeal mixture just until moistened. Stir in corn, drained pineapple, and cheese. Spoon batter into prepare pan.
Bake 35 minutes until a toothpick comes out clean. Cut into squares and serve warm.