  We propose a modified protocol of atomic state teleportation for the scheme
proposed by Bose et al. (Phys. Rev. Lett. 83, 5158 (1999)). The modified
protocol involves an additional stage in which quantum information distorted
during the first stage is fully recovered by a compensation of the damping
factor. The modification makes it possible to obtain a high fidelity of
teleported state for cavities that are much worse than that required in the
original protocol, i.e., their decay rates can be over 25 times larger. The
improvement in the fidelity is possible at the expense of lowering the
probability of success. We show that the modified protocol is robust against
dark counts.
