  We introduce a new dynamical picture, referred to as correlation picture,'
which connects a correlated state to its uncorrelated counterpart. Using this
picture allows us to derive an exact dynamical equation for a general
open-system dynamics with system--environment correlations included. This exact
dynamics is in the form of a Lindblad-like equation even in the presence of
initial system-environment correlations. For explicit calculations, we also
develop a weak-correlation expansion formalism that allows us to perform
systematic perturbative approximations. This expansion provides approximate
master equations which can feature advantages over existing weak-coupling
techniques. As a special case, we derive a Markovian master equation, which is
different from existing approaches. We compare our equations with corresponding
standard weak-coupling equations by two examples, where our correlation picture
formalism is more accurate, or at least as accurate as weak-coupling equations.
