In a medium bowl, cream butter and sugar until very fluffy. Gradually add the flour and rice flour. As the dough gets stiffer, turn it out onto a well floured surface, and knead it until smooth.
Press dough into a 10x15 inch jellyroll pan, score into bars and prick with a fork. Sprinkle remaining sugar over the top, and bake for 30 to 35 minutes in the preheated oven, until golden brown. Cut along scored lines into bars while still warm. Cool before serving.