  Let (S,0) be a germ of complex analytic normal surface. On its minimal
resolution, we consider the reduced exceptional divisor E and its irreducible
components E_i. The Nash map associates to each irreducible component C_k of
the space of arcs through 0 on S the unique component of E cut by the strict
transform of the generic arc in C_k. Nash proved its injectivity and asked if
it was bijective. As a particular case of our main theorem, we prove that this
is the case if E.E_i <0 for any i.
