Preheat oven to 400 F. In a large bowl, mix flour, salt, cayenne pepper, and cheese thoroughly.
Add melted margarine and mix. Chill dough in refrigerator for 20 minutes.
Place dough on a large, floured board. Place a large piece of waxed paper on top of dough or use a heavily-floured rolling pin.
Roll dough to 1/4-inch thick. Remove wax paper. Holding a fork upside down, draw the prongs vertically along dough from top to bottom, making ridges.
With a wide, flat knife cut dough into rectangular shapes 3 x 1 inch. Oil a cookie sheet and place cut cheese on it.
Bake in 400 F oven for 10-12 minutes until cheese straws look dry but not brown.
Let cool. Repeat procedure until all of dough is baked.
Serve at room-temperature. Freezes well. Yields 7 dozen.