  We show that the construction of super-Calogero model with OSp(2|2)
supersymmetry is not unique. In particular, we find a new co-ordinate
representation of the generators of the OSp(2|2) superalgebra that appears as
the dynamical supersymmetry of the rational super-Calogero model. Both the
quadratic and the cubic Casimir operators of the OSp(2|2) are necessarily zero
in this new representation, while they are, in general, nonzero for the
super-Calogero model that is currently studied in the literature. The Scasimir
operator that exists in the new co-ordinate representation is not present in
the case of the existing super-Calogero model. We also discuss the case of N
free superoscillators and superconformal quantum mechanics for which the same
conclusions are valid.
