  The role of a resonant $\nu_e$-$\nu_s$ oscillation is discussed in the event
of a supernova explosion. It is concluded that a significant $\nu_e$-$\nu_s$
mixing may hinder the ability of the supernova to explode. It may also cool the
proto-neutron star too quickly with respect to the observed cooling time of
several seconds. The constraints on the $\nu_e$-$\nu_s$ mixing parameters based
on the above arguments are calculated.
