This paper proposes a new order reduction approach for Roesser state-space model of multidimensional ( n-D) systems based on elementary operations, by inversely applying the basic idea adopted in the new elementary operation approach to the Roesser model realization of n-D systems. It will be shown first that the n-D order reduction problem can be formulated into an elementary operation problem of an n-D polynomial matrix obtained from the coefficient matrices of the given Roesser model. Based on this problem formulation, a basic order reduction procedure and three techniques are presented, by which the intrinsic relationship among the blocks with respect to different variables can be investigated to achieve a further possible order reduction. It turns out that the new proposed approach is applicable to a wider class of Roesser models than the existing reduction approaches and provides a possible way to explore the equivalence between two systems. Examples are given to illustrate the main idea as well as the effectiveness of the proposed approach.