Let Sn = [S(i, j)]1≤i,j≤n and S*n = [S(i + j, j)]1≤i,j≤n where S(i, j) is the Stirling number of the second kind. Choi and Jo [On the determinants of the square-type Stirling matrix and Bell matrix, Int. J. Math. Math. Sci. 2021] obtained the diagonal entries of matrix U in the LU-factorization of S*n for calculating the determinant of S*n, where L = Sn. In this paper, we compute the all entries of U in the LU-factorization of matrix S*n. This implies the identities related to Stirling numbers of both kinds.