In this article, a generalization of a known result about the subdirect sum of two S-SDD (strictly diagonally dominant) matrices is obtained for Σ-SDD matrices. The class of Σ-SDD matrices is a generalization of S-SDD matrices, and it is also a subclass of H-matrices. More precisely, the question of when the subdirect sum and, consequently, the usual sum of two Σ-SDD matrices is an Σ-SDD matrix is studied.