A measurement matrix optimization approach for the linear time-invariant system of which the cyclic index is bigger than 1 (some different Jordan blocks of its Jordan canonical form have the same eigenvalue) was studied. Based on the proving of some cyclic subspace theories and relative properties of root vector chain, the relationship of measurement vectors' linear combination and the system observability was obtained. An approach which can achieve the minimum test cost and assure the system observability at the same time is presented. As the computation example shows, this approach is promising in engineering application as it is simple and straightforward.