  We present results of a large-scale simulation for the Kaon B parameter $B_K$
in quenched lattice QCD with the Kogut-Susskind quark action. Calculating $B_K$
at 1% statistical accuracy for seven values of lattice spacing in the range
$a\approx 0.24-0.04$ fm on lattices up to $56^3\times 96$, we verify a
quadratic $a$ dependence of $B_K$ theoretically predicted. Strong indications
are found that, with our level of accuracy, $\alpha_{\bar{MS}}(1/a)^2$ terms
arising from our one-loop matching procedure have to be included in the
continuum extrapolation. We present $B_K$(NDR, 2 GeV)=0.628(42) as our final
value, as obtained by a fit including the $\alpha_{\bar{MS}}(1/a)^2$ term.
