  The truncated two-point function of the ferromagnetic Ising model on $\mathbb
Z^d$ ($d\ge3$) in its pure phases is proven to decay exponentially fast
throughout the ordered regime ($\beta>\beta_c$ and $h=0$). Together with the
previously known results, this implies that the exponential clustering property
holds throughout the model's phase diagram except for the critical point:
$(\beta,h) = (\beta_c,0)$.
