  We study a system-bath description in the strong coupling regime where it is
not possible to derive a master equation for the reduced density matrix by a
direct expansion in the system-bath coupling. A particular example is a bath
with significant spectral weight at low frequencies. Through a unitary
transformation it can be possible to find a more suitable small expansion
parameter. Within such approach we construct a formally exact expansion of the
master equation on the Keldysh contour. We consider a system diagonally coupled
to a bosonic bath and expansion in terms of a non-diagonal hopping term. The
lowest-order expansion is equivalent to the so-called $P(E)$-theory or
non-interacting blip approximation (NIBA). The analysis of the higher-order
contributions shows that there are two different classes of higher-order
diagrams. We study how the convergence of this expansion depends on the form of
the spectral function with significant weight at zero frequency.
