  The decoherence of two initially entangled qubits in a non-Markovian
reservoir has been investigated exactly without Born Markovian approximation
and rotating-wave approximation(RWA). The non-perturbative quantum master
equation is derived and its exact solution is obtained. The decoherence
behaviors of two qubits, initially entangled in Bell states, has been
investigated in three different cases of parameters. The results show that the
counter-rotating wave terms have great influence on the decoherence behavior,
and there are differences between the exact solution of the Hamiltonian with
RWA and that of the exact Hamiltonian without RWA. It might be improper to take
RWA when the atom is in a non-markovian reservoir.
