It has been shown by Boltianskii [1, 2] that, for a process described by a differential or discrete inclusion, a point which achieves a minimum of a given scalar-valued criterion function will satisfy the support principle [1, 2] if the process under consideration has local sections [1, 2]. The case where local sections do not exist has been studied by the author in [3]. It should be noted that the papers [1-3] deal with scalar minimization problems. In this paper, we shall prove the support principle for a discrete inclusion with a vector-valued criterion function. From the obtained results, it will be easy to derive the support principle for the case where local sections exist as well as for the case where they do not. Also, the discrete minimax problem [2] is included as a special case in our theorem. Our proof of the support principle is based on a general theory of inconsistency of a system of inclusions which is presented (without proofs) in the paragraph §2. It will be easy to see that our method can also be applied to discrete time-lag systems, and discrete distributed parameter systems [3].