When the carrier density is increased in a semiconductor, according to the predictions of Sir Nevil Mott, a transition should occur from an insulating state consisting of a gas of excitons to a conductive electron-hole plasma. This crossover, usually referred to as the Mott transition, is driven by the mutual effects of phase-space filling and Coulomb screening because of the presence of other charges nearby. It drastically affects the optical and electrical characteristics of semiconductors and may, for example, drive the transition from a polariton laser to a vertical cavity surface-emitting laser. Usually, the possible existence of excitonic molecules (or biexcitons) is neglected in the understanding of the Mott transition because the biexciton is supposed to be less robust against screening effects. Here, against common beliefs, we observe that the biexciton in a GaN quantum well is more stable towards the Mott transition than the exciton.