  We prove that sufficiently regular solutions to the wave equation
$\Box_g\phi=0$ on the exterior of the Schwarzschild black hole obey the
estimates $|\phi|\leq C_\delta v_+^{-{3/2}+\delta}$ and $|\partial_t\phi|\leq
C_{\delta} v_+^{-2+\delta}$ on a compact region of $r$ and along the event
horizon. This is proved with the help of a new vector field commutator that is
analogous to the scaling vector field on Minkowski spacetime. This result
improves the known decay rates in the region of finite $r$ and along the event
horizon.
