Abstract: The method given by Michielse and Vorst is reviewed in the paper.The major factors are analyzed,which affect the efficiency of the M ＆ V method.Then a new method for the solution of tridiagonal systems is given based on the divide and conquer computation model.The communication number of the method is half that of the M ＆ V method,and the total data transmissions of the method is reduced to 33% that of the M ＆ V method.The method is implemented on 6 nodes workstation clusters.The results show that compared with the M ＆ V method,the improvement of the new method is up to 40%.