Using the tachyon DBI action proposal for the effective theory of non-coincident D$_p$-brane-anti-D$_p$-brane system, we study the decay of this system in the tachyon channel. We assume that the branes separation is held fixed, i.e. no throat formation, and then find the bounce solution which describe the decay of the system from false to the true vacuum of the tachyon potential. We shall show that due to the non-standard form of the kinetic term in the effective action, the thin wall approximation for calculating the bubble nucleation rate gives a result which is independent of the branes separation. This unusual result might indicate that the true decay of this metastable system should be via a solution that represents a throat formation as well as the tachyon tunneling

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