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Large scale matrix inversion has been used in many domains and block-based Gauss-Jordan (G-J) algorithm as a classical method of large matrix inversion has become the focus of many researchers. Many people show us their parallel version of G-J. But the large parallel granularity in those algorithms restricts the performance of parallel block-based G-J algorithm, especially in the cluster environment consisting of PCs or workstations. This paper presents a fine-grained parallel G-J algorithm to settle the problem presented above. Experiments are made based on YML a framework which enables using different middleware to make large scale parallel computing for its feathers of components reuse, easy programmability for noncomputer professionals. Cluster and Grid environments are based on Grid'5000 platform, France. Experiments show us that the better performance of fine-grained parallel G-J algorithm and YML though overhead existing is a good solution for large scale parallel computing.