  We consider the screening of a magnetic impurity in a $d_{x^2-y^2}$ wave
superconductor. The properties of the $d_{x^2-y^2}$ state lead to an unusual
behavior in the impurity magnetic susceptibility, the impurity specific heat
and in the quasiparticle phase shift which can be used to diagnose the nature
of the condensed state. We construct an effective theory for this problem and
show that it is equivalent to a multichannel (one per node) non-marginal Kondo
problem with linear density of states and coupling constant J. There is a
quantum phase transition from an unscreened impurity state to an overscreened
Kondo state at a critical value J_c which varies with $\Delta_0$, the
superconducting gap away from the nodes. In the overscreened phase, the
impurity Fermi level $\epsilon_f$ and the amplitude $\Delta$ of the ground
state singlet vanish at J_c like $\Delta_0 \exp(- const. / \Delta)$ and J-J_c
respectively. We derive the scaling laws for the susceptibility and specific
heat in the overscreened phase at low fields and temperatures.
