  We present a high-statistics lattice calculation of the kinetic energy
$-\lambda_1/2 m_b$ of the heavy quark inside the $B$-meson and of the
chromo-magnetic term $\lambda_2$, related to the $B^*$--$B$ mass splitting,
performed in the HQET. Our results have been obtained from a numerical
simulation based on 600 gauge field configurations generated at $\beta=6.0$, on
a lattice volume $24^3 \times 40$ and using, for the meson correlators, the
results obtained with the SW-Clover $O(a)$ improved lattice action for the
light quarks. For the kinetic energy we found $-\lambda_1=\langle B \vert \bar
h (i\vec{D})^{2} h \vert B \rangle /(2 M_B )=-(0.09 \pm 0.14)$~GeV$^2$, which
is interesting for phenomenological applications. We also find $\lambda_2= 0.07
\pm 0.01$ GeV$^2$, corresponding to $M^2_{B^*}-M^2_B= 4 \lambda_2= 0.280 \pm
0.060 $ GeV$^2$, which is about one half of the experimental value. The origin
of the discrepancy with the experimental number needs to be clarified.
