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The computational complexity of reasoning within the Dempster-Shafer theory of evidence is one of the major points of criticism this formalism has to face. Various approximation algorithms have been suggested that aim at overcoming this difficulty. This paper presents an improved practical algorithm through reducing the number of focal elements in the belief function involved. In this proposed algorithm, all focal elements of every piece of evidence are classified into dereliction and remainder, and the basic probability assignments of those derelictions are reassigned to the remainders when they are correlative or the dereliction is nested to the remainder. Furthermore, the effect of the dereliction is considered well to influence the combination in this paper, and the computation and accuracy is taken into account to develop this proposed algorithm. Finally, an illustrative example shows that the improved practical algorithm is effective and feasible through comparing with other approximations.