The current international monetary system (IMS) is fragile because the dollar standard is rapidly deteriorating. The dual role of the dollar as the dominant international money and national money cannot easily be reconciled because the US monetary authorities face a conflict between pursuing domestic objectives of employment and inflation, and maintaining the international public good of stable money. To strengthen the IMS, China has advocated the revitalisation of the special drawing rights (SDRs), but SDRs are neither money nor a claim on any international institution; are issued exogenously without any consideration for countries’ external imbalances; and can activate international monies only though bilateral transactions. The historical record of SDRs as international reserves is altogether unimpressive. We propose instead the creation of a supernational bank money (SBM) within the institutional setting of a clearing union. This union would be a fully fledged agreement by participating central banks on specific rules of the game, such as size and duration of overdrafts, designation of countries that would have to bear the burden of external adjustment, and coordination of monetary policies objectives and at expense of the maintenance of the international public good.