Observability of a part of states (partial observability) of unobservable system is very important for fault detection of large systems. Measurement points optimization of unobservable linear discrete systems based on partial observability was studied. It was proved that a sufficient and necessary condition of the partial observability can be obtained by a matrix which is formed by limited observations of the system. Then the rank characteristic of a matrix was proved to be able to be applied to express how observable those partial states are. Finally, an index of this partial observability was presented for the measurement optimization. 