The literature has proposed generalizations and reinterpretations of the Hawkins-Simon condition for macroeconomic stability to off-diagonal matrix elements. These extensions are conceptually relevant for they offer a complementary view of interindustry linkages beyond final or net output influence. The standing extension, however, can be seen to be constructed using the wrong output normalization order. We provide a new and elementary proof for the correct statement that is based upon standard interindustry concepts. Our approach unravels and clarifies the step by step actual mechanisms behind the accounting rules.