The subdirect sum of two square matrices has important applications in the matrix completion problem, the overlapping subdomains of domain decomposition methods, and the global stiffness matrices in finite elements. Applying classification ideas and inequality scaling techniques to the Dashnic-Zusmanovich type matrices, we derive some easily checkable sufficient conditions for determining that the subdirect sum of the Dashnic-Zusmanovich type matrices remains such class of matrices. Numerical examples show that the given conditions are true and valid.