  Decoherence is believed to deteriorate the ability of a purification scheme
that is based on the idea of driving a system to a pure state by repeatedly
measuring another system in interaction with the former and hinder for a pure
state to be extracted asymptotically. Nevertheless, we find a way out of this
difficulty by deriving an analytic expression of the reduced density matrix for
a two-qubit system immersed in a bath. It is shown that we can still extract a
pure state if the environment brings about only dephasing effects. In addition,
for a dissipative environment, there is a possibility of obtaining a dominant
pure state when we perform a finite number of measurements.
