Under the assumption that the wiretapper can get at most r（r < n） independent messages, Cai et al. showed that any rate n multicast code can be modified to another secure network code with transmitting rate n- r by a properly chosen matrix Q^-1. They also gave the construction for searching such an n × n nonsingular matrix Q. In this paper, we find that their method implies an efficient construction of Q. That is to say, Q can be taken as a special block lower triangular matrix with diagonal subblocks being the（n- r） ×（n- r）and r × r identity matrices, respectively. Moreover, complexity analysis is made to show the efficiency of the specific construction. 

Under the assumption that the wiretapper can get at most r（r < n） independent messages, Cai et al. showed that any rate n multicast code can be modified to another secure network code with transmitting rate n- r by a properly chosen matrix Q^-1. They also gave the construction for searching such an n × n nonsingular matrix Q. In this paper, we find that their method implies an efficient construction of Q. That is to say, Q can be taken as a special block lower triangular matrix with diagonal subblocks being the（n- r） ×（n- r）and r × r identity matrices, respectively. Moreover, complexity analysis is made to show the efficiency of the specific construction.