Jets powered by active galactic nuclei appear impressively stable compared with their terrestrial and laboratory counterparts—they can be traced from their origin to distances exceeding their injection radius by up to a billion times1,2. However, some less energetic jets get disrupted and lose their coherence on the scale of their host galaxy1,3. Quite remarkably, on the same scale, these jets are expected to become confined by the thermal pressure of the intra-galactic gas2. Motivated by these observations, we have started a systematic study of active galactic nuclei jets undergoing reconfinement via computer simulations. Here, we show that in the case of unmagnetized relativistic jets, the reconfinement is accompanied by the development of an instability and transition to a turbulent state. During their initial growth, the perturbations have a highly organized streamwise-oriented structure, indicating that it is not the Kelvin–Helmholtz instability, the instability which has been the main focus of the jet stability studies so far4,5. Instead, it is closely related to the centrifugal instability6. This instability is likely to be behind the division of active galactic nuclei jets into two morphological types in the Fanaroff–Riley classification7.