Heat oven to 450 and adjust oven rack to center position.
In a large bowl, combine flour, baking powder, soda, and salt.
Cut in chilled shortening and butter until you have pieces the size of small peas.
Make a well in center of dry ingredients; pour in buttermilk. With a wooden spoon, gently blend dry ingredients into the buttermilk, just until mixture is clumping together. If necessary, add a few more teaspoons of buttermilk.
Transfer dough to a lightly floured board.
Pat out in a circle about 8 inches in diameter and 1/2-inch thick. Using a 2 1/2 to 3-inch biscuit cutter, cut out and place on ungreased baking sheet.
Bake on center oven rack for about 10 to 12 minutes, until tops are browned.