In a large bowl, stir together the flour, cornmeal and sugar. Using a pastry cutter or two knives, cut the butter into the flour until the mixture resembles coarse sand.

Using your hands, sift the mixture through your fingers, pressing the dough slightly so that each time you lift some of the dough, it starts to form larger and larger clumps. When the clumps start to hold together, turn onto a board and knead until the dough holds together and cracks when pressed down.

On a lightly floured board, roll the dough 1/4 inch thick.

Cut into 1 1/2 inch squares and place 1/2 inch apart, on ungreased baking sheets. If desired, press a design into each cookie using the dull edge of a cookie or aspic cutter.

Bake 12 minutes, or until the cookies are barely colored around the edges. Cool on racks.