  Repeated observations of a quantum system interacting with another one can
drive the latter toward a particular quantum state, irrespectively of its
initial condition, because of an {\em effective non-unitary evolution}. If the
target state is a pure one, the degree of purity of the system approaches
unity, even when the initial condition of the system is a mixed state. In this
paper we study the behavior of the purity from the initial value to the final
one, that is unity. Depending on the parameters, after a finite number of
measurements, the purity exhibits oscillations, that brings about a lower
purity than that of the initial state, which is a point to be taken care of in
concrete applications.
