We begin by decomposing the square lattice down into plaquettes arranged in a checkered pattern (such that the plaquettes only overlap vertex-wise but not edge-wise). Since the spin model is fully-frustrated, each plaquette must contain exactly one or three negative interactions. If the plaquette contains three negative interactions, then no bonds can be formed. However, if the plaquette contains one negative interaction, then two parallel bonds can be formed (perpendicular to the negative edge) with probability p = 1 − − e − − 4 β β , where β β is the inverse temperature of the spin model.