Decay of type 0 NS5-branes to nothing

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.