  We study the improvement of staggered fermions using hypercubically smeared
(HYP) links. We calculate the strange quark mass and the kaon B-parameter,
$B_K$, in quenched QCD on a $16^3 \times 64$ lattice at $\beta=6.0$. We find
$m_s(\bar{\rm MS},2 {\rm GeV})=101.2\pm1.3\pm4 $MeV and $B_K(\bar{\rm MS},2
{\rm GeV}) = 0.578 \pm 0.018\pm 0.042$, where the first error is from
statistics and fitting, and the second from using one-loop matching factors.
The scale ($1/a=1.95$GeV) is set by $M_\rho$, and $m_s$ is determined using the
kaon mass. Comparing to quenched results obtained using unimproved staggered
fermions and other discretizations, we argue that the size of discretization
errors in $B_K$ is substantially reduced by improvement.
