Abstract: Based on high-dimensional Markovian model and combining the basic conception of states for traditional Markov chain, the new definitions of accessibility, interoperability, first arrival time and its probability for multivariate Markovian model are defined, and the notion of recurrence, ergodicity and periodicity are given by these definitions, too. Moreover, the Chapman-Kolmogorov equation of multivariate Markovian model is proposed, and using this equation study on basic property of relationships among the states. The conclusion show that there are symmetry, transitivity, identical recurrence and period in relationships among states under interoperable state condition.