It is well-known D. Carlson, T. Markham, Schur complements of diagonally dominant matrices, Czech. Math. J. 29 (104) (1979) 246–251, 1 that the Schur complement of a strictly diagonally dominant matrix is strictly diagonally dominant. Also, if a matrix is an H-matrix, then its Schur complement is an H-matrix, too J. Liu, Y. Huang, Some properties on Schur complements of H-matrices and diagonally dominant matrices, Linear Algebra Appl. 389 (2004) 365–380, 8. Recent research showed that the same type of statement holds for some special subclasses of H-matrices, see, for example, Liu et al. J. Liu, Y. Huang, F. Zhang, The Schur complements of generalized doubly diagonally dominant matrices, Linear Algebra Appl. 378 (2004) 231–244. The aim of this paper is to show that the proof of these results can be significantly simplified by using “scaling” approach as in Zhang et al. F. Zhang et al., The Schur Complement and its Applications, Springer, New York, 2005 and to give another invariance result of this type.