  We provide a new approach to open quantum systems which is based on the
Feshbach projection method in an appropriate Hilbert space. Instead of looking
for a master equation for the dynamical map acting in the space of density
operators we provide the corresponding equation for the evolution in the
Hilbert space of the system. Its solution enables one to construct a legitimate
quantum evolution (completely positive and trace preserving). The big advantage
of this approach is the ability of performing a consistent approximation which
creates notorious problems in the standard Nakajima-Zwanzig approach. The new
scheme is illustrated by well known spin-boson model beyond rotating wave
approximation.
