In a large bowl, stir together the flour, baking powder, salt and baking soda. Using a pastry blender, cut in cold butter and shortening till mixture resembles coarse crumbs. Stir in the cheese. Make a well in the center of the flour mixture. Add buttermilk all at once. Using a fork, stir just till moistened. (Do not overwork the dough.)
Turn dough out onto a lightly floured surface. Knead dough by folding and gently pressing dough for 4 to 6 strokes or just till dough holds together. Pat or lightly roll dough into a 12-inch square. Cut the dough with a floured knife into sixteen 3-inch squares.
Arrange biscuits on ungreased baking sheets. Bake in a 450 degree oven for 10 to 12 minutes or till golden. Remove biscuits from baking sheet. Serve warm.