  Supervisor reduction procedure can be used to construct the reduced
supervisor with a reduced number of states in discrete-event systems. The main
concepts which are used in this procedure are control consistency of states,
control cover, induced supervisor, and normality of the reduced supervisor
w.r.t. the original supervisor. In this paper, it is proved that the reduced
supervisor, constructed by the proposed method in [9], preserves the
observation properties, i.e. normality and relative observability, by self
looping corresponding unobservable events at some states of the reduced
supervisor. This property can be applied to find a natural projection, under
which the supervisor is relative observable.
