Place a slice of cheese on one half of each muffin and top with a slice of bacon. Set aside.
Heat the margarine in a large nonstick skillet until hot. Crack the eggs into the pan, lower the heat, and fry. Try to keep the eggs as round as you can by pushing them with a wooden spoon to keep the eggs from spreading out in the pan.
Flip the eggs after a couple of minutes, when whites seem solidified. Cook 1 or 2 minutes more.
Place 1 egg on each piece of bacon. Cover the egg with the other half of muffin; serve immediately.