Diffeomorphism on the horizon as an asymptotic isometry of the Schwarzschild black hole

It is argued that the diffeomorphism on the horizontal sphere can be regarded as a non-trivial asymptotic isometry of the Schwarzschild black hole. We propose a new boundary condition of asymptotic metrics near the horizon and show that the condition admits the local time shift and diffeomorphism on the horizon as the asymptotic symmetry.