Experimental evidence was found in JET plasmas, of a new instability at the onset of minor disruptions. This instability is observed during the growth of the well known m/n = 2/1 magnetic island and is localized close to it, behaving as a secondary instability to the island. The large heat fluxes towards the plasma edge, characteristic of minor disruptions, occur during the low rotation phase of the magnetic island at a time the amplitude of the secondary instability suffers a large increase. No poloidal or toroidal mode numbers could be assigned to the secondary instability.