  It is known that a generic star vector field $X$ on a $3$ or $4$-dimensional
manifold is such that its chain recurrence classes are either hyperbolic, or
singular hyperbolic ([MPP] and [GSW]). Palis conjectured that every vector
field must be approximated either by singular hyperbolic vector fields or by
vector fields with homoclinic tangencies or heterodimensional cycles
(associated to periodic orbits). We give a counter example in dimension $5$
(and higher). We present here an open set of star vector fields on a
$5$-dimensional manifold for which two singular points with different indices
belong (robustly) to the same chain recurrence class. This prevents the class
to be singular hyperbolic, showing that the results in [MPP] can not be
extended to higher dimensions and thus contradicting the conjecture by Palis.
