  We present the results of a numerical calculation of semi-leptonic form
factors relevant for heavy flavour meson decays into light mesons, at
$\beta=6.4$ on a $24^3 \times 60$ lattice, using the Wilson action in the
quenched approximation. We obtain $f^+_K(0)=0.65\pm 0.18$, $V(0)=0.95\pm 0.34$,
$A_1(0)=0.63\pm 0.14 $ and $A_2(0)=0.45\pm 0.33 $. We also obtain
$A_1(q^2_{max})=0.62\pm 0.09$, $V(0)/A_1(0)=1.5\pm 0.28 $ and
$A_2(0)/A_1(0)=0.7\pm 0.4$. The results for $f^+_K(0)$, $V(0)$ and $A_1(0)$ are
consistent with the experimental data and with previous lattice determinations
with larger lattice spacings. In the case of $A_2(0)$ the errors are too large
to draw any firm conclusion. We have also extrapolated the form factors to the
B meson, showing a behaviour compatible with the predictions by the heavy quark
effective theory (HQET). Within large uncertainties, our results suggest that
$A_2/A_1$ increases with the heavy quark mass. We also get very rough estimates
for the partial decay widths $B \rightarrow \pi l \nu_l)=\vert V_{ub} \vert^2
(12 \pm 8) 10^{12} s^{-1}$ and $\Gamma(B \rightarrow \rho l \nu_l)=\vert V_{ub}
\vert^2 (13 \pm12) 10^{12} s^{-1}$, which can be used to give upper bounds on
the rates
