Computation and data decompositions are key factors of affecting the performance of parallel programs running on distributed memory multicomputers. This paper presents a theoretical framework of data space fusion and an effective global computation and data decomposition approach based on it, which can be used to solve computation and data decomposition problems on distributed memory multicomputers. The approach can exploit the parallelism of computation space as high as possible, use the technique of data space fusion to optimize data distribution, and search the optimizing global computation and data decompositions. The approach can also be integrated with data replication and offset alignment naturally, and therefore can make the communication overhead as low as possible. Experimental results show that the approach presented in the paper is effective.