Relaxed technique is one of the main techniques for improving convergence rate of splitting iterative method. Based on existing parallel multisplitting methods, we have deeply studied the convergence of the relaxed multisplitting method associated with TOR multisplitting for solving the linear system whose coe±cient matrix is an H-matrix. More- over, theoretical analysis have shown that the convergence domain of the relaxed parameters is weaker and wider, and numerical examples on an MPP clearly show that the new conver- gent results are e±cient.