When a phosphate-buffered saline (PBS) solution is exposed to atmospheric-pressure plasmas generated in air, hydrogen peroxide H2O2 in the solution is known to be decomposed by hypochlorite OCl-, which is formed in the solution from reactions between chlorine ions Cl- present in the PBS solution and plasma-generated reactive oxygen species. Global numerical simulations of liquid-phase chemical reactions were performed to identify the reaction mechanisms of H2O2 decomposition by solving known liquid-phase chemical reactions self-consistently. It has been confirmed that the decomposition of H2O2 is indeed mostly due to the presence of OCl- in the solution. However, this study has also found that, in the presence of abundant hydroxyl (OH) radicals, the most efficient H2O2 decomposition pathway can be a series of reactions that we call a chlorine monoxide cycle, where OCl- first reacts with hydroxyl radical OH to generate chlorine monoxide ClO, which then decomposes HOCl, rather than OCl- directly decomposing H2O2. The chlorine monoxide cycle generates OH as one of its byproducts, so once this cycle is initiated, it continues until either ClO- or H2O2 runs out, as long as none of the intermediates are scavenged by other reactions.