Abstract: Using non linear storage scheme, an SIMD computer can provide conflict free access of several access patterns and then get nice global performance, in which the number of processors is the same as that of parallel memories. A general method of designing such SIMD computer is presented in this paper. In the case of a given storage scheme, a parallel architecture can be designed for a definite set of templates, which can provide both memory access conflict free and the interconnection conflict free. At first, the template is defined with Boolean vector space. The relationship between a template and an LC permutation is given. Then, the method to design the local address generation and the enhanced indirect binary n cube network is brought forward. Every template can be accessed in memory simultaneously and can be aligned by the network with one pass, thus allowing both the processors and memories to achieve the highest utilization.