The BMS algorithm from Coding Theory has good decoding efficiency and error-correcting capability, and current work usually focuses on the case of graded orderings. With the analysis on the essential characteristics of lexicographical and graded orderings, a termination criterion of BMS algorithm for the lexicographical ordering is designed by using the elimination property of Gröbner bases, which are closely related to the BMS algorithm, and an implementation-oriented description for the algorithm based on this criterion is also provided. Experimental results verify the effectiveness of the proposed termination criterion, and the new criterion matches the original theoretical one in the algorithm.