  The canonical formalism of the (2+2) formulation of general relativity of 4
spacetime dimensions is studied under no symmetry assumptions, where the
spacetime is viewed as a local product of a 2 dimensional base manifold of
Lorentzian signature with the vertical space as its complement. The affine null
parameter is chosen as the time coordinate whose level surfaces are 3
dimensional spacelike hypersurfaces. From the first-order action principle,
Hamilton's equations of motion and the constraints are obtained, which are
found to be equivalent to the Einstein's equations. The constraint algebra is
also presented, which has interesting subalgebras such as the infinite
dimensional Lie algebra of the diffeomorphisms of the 2 dimensional vertical
space, infinite dimensional Virasoro algebra associated with the 2 dimensional
base manifold, and an analog of supertranslation. The symmetry algebra may be
viewed as a generalization of the BMS or Spi group to a finite distance.
