  The non-Markovian master equation for open quantum systems is obtained by
generalization of the ordinary Zwanzig-Nakajima (ZN) projection technique. To
this end, a coupled chain of equations for the reduced density matrices of the
bath $\varrho_{B}(t)$ and the system $\varrho_{S}(t)$ are written down. A
formal solution of the equation for $\varrho_{B}(t)$, having been inserted in
the equation for the reduced density matrix of the system, in the 2-nd
approximation in interaction yields a very specific extra term in the
generalized master equation. This term, being nonlinear in $\varrho_{S}(t)$, is
related to the intrinsic bath dynamics and vanishes in the Markovian limit. To
verify the consistence and robustness of our approach, we applied the
generalized ZN projection scheme to a simple dephasing model. It is shown that
consideration of the lowest order in interaction is insufficient to describe
time evolution of the system coherence adequately. We explain this fact by
analyzing the exact and approximate forms of $\varrho_{B}(t)$ and give some
hints how to take the dynamic correlations (which originate from the spin-bath
coupling) into account.
