A lattice structure of multidimensional (MD) linear-phase paraunitary filter banks (LPPUFBs) is proposed, which makes it possible to design such filter banks in a systematic manner. The proposed structure can produce MD-LPPUFBs whose filters all have the region of support N(M Xi), where M and Xi are the decimation and an integer diagonal matrices, respectively, and ni (N) is the set of integer vectors in the fundamental parrallelpiped of N. Since our proposed system structurally restricts both the paraunitary and linear-phase properties, an unconstrained optimization process can be used to design MD-LPPUFBs. Some design examples will show the significance.