If theS-meson is assumed to be a baryonium state composed of an isospin one diquark and antidiquark, it will be produced in\(\bar pp\) reactions as a mixture ofI=0 andI=1 baryonium states. The experimentally observed large ratio of the cross sections of the reactions\(\bar pp \to S \to \bar pp\) and\(\bar pp \to S^0 \to \bar nn\) is then explained on basis of quark additivity and conservation of isospin in thes-channel. The model predicts:\(\sigma (\bar pp \to S^0 \to \bar pp):\sigma (\bar pp \to S^0 \to \bar nn):\sigma (\bar pn \to S^ - \to \bar pn) = 25:1:16\).