  The truncated two-point function of the nearest-neighbor ferromagnetic Ising
model on $\mathbb Z^d$ ($d\ge3$) in its pure phases is proven to decays
exponentially fast throughout the ordered regime ($T<T_c$). Together with known
results, this implies that the exponential clustering property holds throughout
the model's phase diagram except for the critical point: $(T,h) = (T_c,0)$.
