In a large mixing bowl, beat butter with the larger amount of sugar until smooth.

Gradually add all-purpose and rice flours until well combined. Spread in a 9 by 13 inch baking dish. Bake in a 275F oven until pale golden, 55 to 65 minutes. Place on racks and let cool for 10 minutes. Sprinkle lightly with sugar, then cut into 24 bars. Let cool completely. Serve.