  We analyze perturbative dynamics of a composite system consisting of a
quantum mechanical system and an environment by the renormalization group (RG)
method. The solution obtained from the RG method has no secular terms and
approximates the exact solution for a long time interval. Moreover, the RG
method causes a reduction of the dynamics of the composite system under some
assumptions. We show that this reduced dynamics is closely related to a quantum
master equation for the quantum mechanical system. Then, we compare this
dynamics with the exact dynamics in an exactly solvable spin-boson model.
