  It is well known that tachyonic vacua in an asymptotically Anti-de Sitter
(AdS) space-time are classically stable if the mass squared is at or above the
Breitenlohner and Freedman (BF) bound. We study the quantum stability of these
tachyonic vacua in terms of instantons. We find a series of exact instanton
solutions destabilizing tachyonic state at or above the BF bound in
asymptotically AdS space. We also give an analytic formula for the decay rate
and show that it is finite. Comparing our result with the well-known algebraic
condition for the stability, we discuss stability conditions of tachyonic vacua
at or above the BF bound.
