  We consider a four dimensional space-time symmetry which is a non trivial
extension of the Poincar\'e algebra, different from supersymmetry and not
contradicting {\sl a priori} the well-known no-go theorems. We investigate some
field theoretical aspects of this new symmetry and construct invariant actions
for non-interacting fermion and non-interacting boson multiplets. In the case
of the bosonic multiplet, where two-form fields appear naturally, we find that
this symmetry is compatible with a local U(1) gauge symmetry, only when the
latter is gauge fixed by a `t Hooft-Feynman term.
