  For a symmetric system, we want to study the problem of crossing an
hypersurface in the neighborhood of a given point, when we suppose that all of
the available vector fields are tangent to the hypersurface at the point.
Classically one requires transversality of at least one Lie bracket generated
by two available vector fields. However such condition does not take into
account neither the geometry of the hypersurface nor the practical fact that in
order to realize the direction of a Lie bracket one needs three switches among
the vector fields in a short time. We find a new sufficient condition that
requires a symmetric matrix to have a negative eigenvalue. This sufficient
condition, which contains either the case of a transversal Lie bracket and the
case of a favorable geometry of the hypersurface, is thus weaker than the
classical one and easy to check. Moreover it is constructive since it provides
the controls for the vector fields to be used and produces a trajectory with at
most one switch to reach the goal.
