  We present the results of a high statistics lattice calculation of hadronic
form factors relevant for $D-$ and $B-$meson semi-leptonic decays into light
pseudoscalar and vector mesons. The results have been obtained by averaging
over 170 gauge field configurations, generated in the quenched approximation,
at $\beta=6.0$, on a $18^3 \times 64$ lattice, using the $O(a)$-improved
SW-Clover action.From the study of the matrix element $<K^-\vert J_\mu \vert
D^0>$, we obtain $f_+ (0)=0.78\pm 0.08$ and from the matrix element $<\bar K^{*
0}\vert J_\mu \vert D^+>$ we obtain $V(0)=1.08\pm 0.22$, $A_1(0)=0.67\pm 0.11$
and $A_2(0)=0.49\pm 0.34$. We also obtain the ratios $V(0)/A_1(0)=1.6\pm 0.3$
and $A_2(0)/A_1(0)= 0.7\pm 0.4$. Our predictions for the different form factors
are in good agreement with the experimental data, although, in the case of
$A_2(0)$, the errors are still too large to draw any firm conclusion. With the
help of the Heavy Quark Effective Theory (HQET) we have also extrapolated the
lattice results to $B$-meson decays. The form factors follow a behaviour
compatible with the HQET predictions. Our results are in agreement with a
previous lattice calculation, performed at $\beta=6.4$, using the standard
Wilson action.
