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This paper describes a lattice structure and a design for orthogonal and biorthogonal multiwavelets. First, we factorize the polyphase matrices of symmetric-antisymmetric multifilter bank into elementary low-order building blocks. Second, we transform a tree-structured multiwavelet system into an equivalent scalar filter bank in order to design optimal multifilter banks. Simulation results show that the proposed orthogonal and biorthogonal multiwavelets have superior performance to the popular multiwavelet SA4 and the (9,7)-tap scalar wavelet.