  We obtain a lower bound for the normalised height of a non-torsion
hypersurface $V$ of a C.M. abelian variety $A$ which is a refinement of a
precedent result. This lower bound is optimal in terms of the geometric degree
of $V$, up to an absolute power of a ``log'' (independant of the dimension of
$A$). We thus extend the results of F. Amoroso and S. David on the same problem
on a multiplicative group $\mathbb{G}_m^n$. When $A$ is an elliptic curve and
$V=\bar{P}$ is the set of conjugates of a non torsion $\bar{k}$-point, we
reobtain the result of M. Laurent on the elliptic Lehmer's problem.
