If quark matter is energetically favored over nuclear matter at zero temperature and pressure, then it has long been expected to take the form of strange quark matter (SQM), with comparable amounts of u, d, and s quarks. The possibility of quark matter with only u and d quarks (udQM) is usually dismissed because of the observed stability of ordinary nuclei. However, we find that udQM generally has lower bulk energy per baryon than normal nuclei and SQM. This emerges in a phenomenological model that describes the spectra of the lightest pseudoscalar and scalar meson nonets. Taking into account the finite size effects, udQM can be the ground state of baryonic matter only for baryon number A>A_{min} with A_{min}≳300. This ensures the stability of ordinary nuclei and points to a new form of stable matter just beyond the periodic table.