  Recently, we presented a new class of quantum-mechanical Hamiltonians which
can be written as the $F^{th}$ power of a conserved charge: $H=Q^F$ with
$F=2,3,...\,.$ This construction, called fractional supersymmetric quantum
mechanics, was realized in terms of a paragrassmann variable $\theta$ of order
$F$, which satisfies $\theta^F=0$. Here, we present an alternative realization
of such an algebra in which the internal space of the Hamiltonians is described
by a tensor product of two paragrassmann variables of orders $F$ and $F-1$
respectively. In particular, we find $q$-deformed relations (where $q$ are
roots of unity) between different conserved charges. (To appear in
"Mod.Phys.Lett.A")
