  We are concerned here with Lehmer's problem in dimension 2 ; we give a lower
bound for the height of a non-torsion point of $G\_m^2$ on a non-torsion curve
defined over $Q$, depending on the degree of the curve only. We have first been
inspired by \cite{Am-Da3}; we develop a new approach, inherent in the dimension
two (or more precisely the codimension two), and then obtain a better result
where the error's term is improved significantly, moreover we give an explicit
expression for the constant.
