  We present a calculation of $f_B$ in the static limit, obtained by numerical
simulation of quenched QCD, at $\beta=6.2$ on a $18^3 \times 64$ lattice, using
the SW-Clover quark action. The decay constant has been extracted by studying
heavy(static)-light correlation functions of different smeared operators, on a
sample of 220 gauge field configurations. We have obtained $f_B^{static}=(290
\pm 15 \pm 45)$ MeV, where the first error comes from the uncertainty in the
determination of the matrix element and the second comes from the uncertainty
in the lattice spacing. We also obtain $M_{B_s}-M_{B_d}= (70 \pm 10)$ MeV and
$f^{stat}_{B_s}/f^{stat}_{B_d}=1.11(3)$. A comparison of our results with other
calculations of the same quantity is made.
