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We analyze possible local extensions of the Poincar\'e symmetry in light-conegravity in four dimensions. We use a formalism where we represent the algebraon the two physical degrees of freedom, one with helicity $2$ and the otherwith helicity $-2$. The representation is non-linearly realized and one of thelight-cone momenta is the Hamiltonian, which is hence a non-linear generator ofthe algebra. We find that this can be locally realized and the Poincar\'ealgebra extended to the BMS symmetry without any reference to asymptoticlimits.

BMS algebra as an extension of the Poincar\'e symmetry in light-cone gravity