  We present results for the kaon $B$-parameter $B_K$ from a sample of $200$
configurations using the Wilson action and $460$ configurations using the
SW-Clover action, on a $18^3 \times 64$ lattice at $\beta=6.0$. We compare
results obtained by renormalizing the relevant operator with different
``boosted" values of the strong coupling constant $\alpha_s$. In the case of
the SW-Clover action, we also use the operator renormalized non-perturbatively.
In the Wilson case, we observe a strong dependence of $B_K$ on the prescription
adopted for $\alpha_s$, contrary to the results of the Clover case which are
almost unaffected by the choice of the coupling. We also find that the matrix
element of the operator renormalized non-perturbatively has a better chiral
behaviour. This gives us our best estimate of the renormalization group
invariant $B$-parameter, $\hat B_K=0.86 \pm 0.15$.
