The final stage of a black hole evaporation due to the Hawking effect is studied. One finds that, including the effects of quantum gravity, a black hole does not evaporate completely losing its energy steadily to a flux of created particles, but rather decays via a change in topology into an asymptotically flat space and an object which is a closed Friedmann Universe. This process is a genuine non-perturbative effect of quantum gravity and becomes the dominant “channel” of a black hole decay for black holes with masses slightly larger than the Planck mass Mp=1019 GeV. We calculate the decay rate of a Schwarzchild black hole with the mass M and discuss other decay “channels” by topology change. An explicit instanton mediating the decay is constructed by matching the Schwarzschild and the “wormhole” Friedmann instantons on the minimal sphere which is a Euclidean section of the event horizon. We show, as an example, that the decay process is mediated in the semi-classical approximation by the gravitational-axionic instanton. However, we argue that the phenomenon discussed in this paper does not depend on the particular instanton approximation and should be discussed in the framwork of the second quantization of interacting geometry suggested in Ref. 17. It is argued that in the more general setting of the Wheeler-De Witt equation, the wave functional describing a black hole is not gaussian because of the existence of an unstable mode.