The existence of a positive balanced growth solution for the discrete dynamic input-output (IO) model is studied. Previous work in the area invariable assumed unrealistic restrictions on the matrices A or B, such as regularity or irreducibility. In our work these restrictions are not imposed. We find that in the realistic case of reducible A, a balanced growth solution exists if each sector depends on all others for either its current account or its capital inputs. If this condition is not satisfied a balanced growth solution may still exist. Conditions for its existence relate the overall growth rate to the growth rates which groups of sectors would have if they were isolated from the rest of the economy.