  The near-horizon limit of the extremal (weakly) isolated horizon is obtained
under the Bondi-like coordinates. For the vacuum case, explicit coordinate
transformation relating the near-horizon metric under the Bondi-like
coordinates and the standard Poincar\'e-type or global near-horizon metric of
the extremal Kerr black hole is found, which shows that the two geometries are
the same. Combined with the known thermodynamics of the (weakly) isolated
horizon, it is argued that the Kerr/CFT correspondence can be generalized to
the case of a large class of non-stationary extremal black holes.
