Preheat the oven to fan oven 180C, 160C, gas mark 4. Lightly grease a 19x29cm tin with butter.
Sift the flour and cornflour together into a big mixing bowl. Stir in the ground rice or semolina and sugar and then beat in the butter. Alternatively you can put all the ingredients in a food processor and mix to a smooth dough.
Press the shortbread dough into the tin and level the surface with the back of a spoon. Prick all over with a fork. Bake for 30-40 minutes until set and just golden. Remove from the oven, cut into 24 pieces and leave to cool and firm up in the tin. Store in an airtight container for 2-3 days.