Finding good upper bound for the size of m-ary t-symmetric error correcting codes (t-sEC/AUED codes) codes is the main problem in the coding theory of m-ary t-sEC/AUED codes. Based on the method of Lagrange multipliers, We shall derive an upper bound on the size of m-ary t-sEC/AUED in this paper. Some examples achieved this upper bound are also given in this paper.