CCAST, World Lab, Beijing 100080, Peoples R China
; Chinese Acad Sci, Inst High Energy Phys, Beijing 100039, Peoples R China
; Chinese Acad Sci, Inst Theoret Phys, Beijing 100080, Peoples R China
; Max Planck Inst Gravitat Phys, D-14476 Golm, Germany
We present the Noether-charge realization of the diffeomorphism invariance of the gravitational theory in the covariant phase space formalism. With the help of the null tetrad well defined on the horizon, it is shown that the central term vanishes for the reduced diffeomorphism algebra on the Killing horizon with respect to a large class of vector fields in the vacuum general relativity.