  The strong system-bath correlation is a typical initial condition in many
condensed matter and some quantum optical systems. Here, the dynamics of a spin
interacting with a spin bath through an intermediate spin are studied. Initial
correlations between the spin and the intermediate spin are taken into account.
The exact analytical expression for the evolution operator of the spin is
found. Furthermore, correlated projection superoperator techniques are applied
to the model and a time-convolutionless master equation to second order is
derived. It is shown that the time-convolutionless master equation to second
order reproduces the exact dynamics for time-scales of the order 1/{\gamma},
where {\gamma} is the coupling of the central spin to the intermediate spin. It
is found that there is a strong dependence on the initial system-bath
correlations in the dynamics of the reduced system, which cannot be neglected.
