  We show that we can combine the (complex, self-dual) BMS vector fields with
the recently defined BMS twistors to obtain a new supersymmetric extension of
the BMS symmetries at null infinity. We compare our construction to other
supersymmetric extensions of the BMS algebra proposed in the context of
supergravity. Unlike the standard constructions the anticommutator in our
superalgebra generates all the BMS vector fields including the Lorentz
transformations. We also show that there exists a projection from our BMS Lie
superalgebra to the global subalgebra of the Neveu-Schwarz supersymmetries on a
2-sphere, which are commonly considered in string theory and 2-dimensional
conformal field theory.
