  The form of realistic space-time supersymmetry is fixed, by
Haag-Lopuszanski-Sohnius theorem, either to the familiar form of Poincare
supersymmetry or, in massless case, to that of conformal supersymmetry. We
question necessity for such strict restriction in the context of theories with
broken symmetries. In particular, we consider parabose N=4 algebra as an
extension of conformal supersymmetry in four dimensions (coinciding with the,
so called, generalized conformal supersymmetry). We show that sacrificing of
manifest Lorentz covariance leads to interpretation of the generalized
conformal supersymmetry as symmetry that contains, on equal footing, two
"rotation" groups. It is possible to reduce this large symmetry down to
observable one by simply breaking one of these two SU(2) isomorphic groups down
to its U(1) subgroup.
