  The perturbative vacuum of type 0 string theory is unstable due to the
existence of the closed string tachyon. This instability can be removed by S^1
compactification with twisted boundary condition for the tachyon field. We show
that even in this situation unwrapped NS5-branes are unstable and decay to
bubbles of nothing smoothly without tunneling any potential barrier. We discuss
a relation between the closed string tachyon condensation and the instability
of NS5-branes.
