  We prove for a generic star vector field $X$ that, if for every chain
recurrent class $C$ of $X$ all singularities in $C$ have the same index, then
the chain recurrent set of $X$ is singular hyperbolic. We also prove that every
Lyapunov stable chain recurrent class of $X$ is singular hyperbolic. As a
corollary, we prove that the chain recurrent set of a generic 4-dimensional
star flow is singular hyperbolic.
