  Structure of the state-vector space for a system consisting of one mode
parabose and one mode parafermi degree of freedom with the same parastatistics
order $p$ is studied and a complete, orthonormal set of basis vectors in this
space is constructed. There is an intrinsic double degeneracy for state vectors
with $m$ parabosons and $n$ parafermions, where $m \not= 0$, $n \not= 0$, and
$n \not= p$. It is also shown that the degeneracy plays a key role in
realization of exact supersymmetry for such a system.
