In this paper, we will talk about the branch number of matrix of order n over ring ℤ/(2^m), while there are few papers on it, but there are some crypotosystems based on the ring ℤ/(2^m). In 2017 , Qu etc only proved that there no MDS matrix (i.e. the branch number of matrix is n + 1) on the ring ℤ/(2^m). We firstly introduce the DSMDS (LSMDS) matrix (i.e. the differential (linear)separable branch number of matrix is n) and prove there exist such matrice of order 2;3;4. Secondly, we give a sufficient and necessary condition of DSMDS (LSMDS) matrix, respectively. Thirdly, we show there are no DSMDS (LSMDS) matrix of order n for n ≥ 5 using conditons got above. So, we should study the upper bound of the branch number of a matrix. Finally, we give another depiction of the branch number of a matrix and conjecture a new tight upper bound of it, which smaller than the known upper bound given in 2008, for n ≥ 6. We prove that it is true when n = 6,7 and leave it as an open problem for n ≥ 8.