  The Separatrix Theorem of C. Camacho and P. Sad guarantees the existence of
invariant curve (separatrix) passing through the singularity of germ of
holomorphic foliation on complex surface, when the surface underlying the
foliation is smooth or when it is singular and the dual graph of resolution
surface singularity is a tree. Under some assumptions, we obtain existence of
separatrix even when the resolution dual graph of the surface singular point is
not a tree. It will be necessary to require an extra condition of the
foliation, namely, absence of saddle-node in its reduction of singularities.
