Sift together flour, sugar, and cornstarch in a small mixing bowl; set aside.
Cream butter; gradually stir in reserved flour mixture. Shape dough into a ball, and chill 1 to 2 hours.
Shape dough into 1-inch balls, and place 2 inches apart on ungreased cookie sheets. Press a lightly floured fork in center of each ball to flatten to 1/2-inch thickness. Bake at 300° for 20 to 22 minutes. Cool slightly on cookie sheets; remove from cookie sheets, and cool completely on wire racks.