  BMS group (and it's various generalizations) at null infinity have been
studied extensively in the literature as the symmetry group of asymptotically
flat spacetimes. The intricate relationship between soft theorems and the BMS
symmetries have also motivated the definition of such asymptotic symmetries to
time-like infinity. Although the vector fields that generate the (generalized)
BMS algebra at time-like infinity was defined in the literature, the algebra
has not been investigated. In this paper, we fill this gap. We show that the
super-translations and vector fields that generate sphere diffeomorphisms close
under the modified Lie bracket proposed by Barnich et al.
