In this paper one extends results of Bendixson [I] and Dumortier [2] about the germs of vector fields at the origin of IR2, which is assumed to be an singularity isolated from other singularities and periodic orbits as well. As a new tool, one uses minimal centred curves, which are curves surrounding the origin, with a minimal number of contact points with the vector field. A similar notion was introduced by Le Roux in [1]. It is noticeable that the arguments are essentially topological, with no use of a desingularization theory, as in [2] for instance.