### A class of non-rational surface singularities with bijective Nash map

Let $(\mathcal{S},0)$ be a germ of complex analytic normal surface. On its minimal resolution, we consider the reduced exceptional divisor $E$ and its irreducible components ${E}_{i}$, $i\in I$. The Nash map associates to each irreducible component ${C}_{k}$ of the space of arcs through $0$ on $\mathcal{S}$ 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 $E\xb7{E}_{i}\<0$ for any $i\in I$.