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In this paper, we propose a new method for solving linear algebraic systems based on the KSOR method. The new approach introduces a new coefficient in the assumed updated section from the KSOR method. It obtains the same solution as KSOR for a given linear algebraic system, but in order to get this, we have to modify the diagonal of the coefficient matrix of the initial system. The new method reaches the solution in fewer steps than KSOR on certain examples, but we have an additional step for the modification mentioned above with O(m) complexity, while a normal step of iteration has O (m 2) complexity, so overall our method has better performances than KSOR method. Furthermore, on certain examples, the spectral radius of the iteration matrix of the new method is strictly less than the one of KSOR and MKSOR methods. [ABSTRACT FROM AUTHOR]