  It has been conjectured that in head-on collisions of neutron stars (NSs),
the merged object would not collapse promptly even if the total mass is higher
than the maximum stable mass of a cold NS. In this paper, we show that the
reverse is true: even if the total mass is {\it less} than the maximum stable
mass, the merged object can collapse promptly. We demonstrate this for the case
of NSs with a realistic equation of state (the Lattimer-Swesty EOS) in head-on
{\it and} near head-on collisions. We propose a ``Prompt Collapse Conjecture''
for a generic NS EOS for head on and near head-on collisions.
