Abstract: In order to avoid producing  many equally most parsimonious trees, Li (1990)  developed  a  new  cladistic  method,  the  Median  Elimination Series (MES), to construct a single cladogram for a given data set. However, we found that Li's method can produce more than one tree if two or more taxa have the same advancement index (which is the total number of apomorphies for a taxon in a given data set), because there is no objective method to decide which taxon should be connected first and different orders of connection can produce different trees.   Li claimed that the result produced by his method did not apply the principle of simplicity (parsimony). Nevertheless, Zhang (1991) recognised that Li's meth- od actually accepted the principle of parsimony. Here we demonstrated that Li's method also can produce the minimum-length trees.   We conclude that Li's method could produce more than one tree and the tree(s) may be the minimum-length possible. However, the length of tree(s) depends on the order of connection of the taxa. The major problems in using Li's methodare discussed.