  Recent studies show that for systems with four identical fermions in the
$j=9/2$ shell two special states, which have seniority $v=4$ and total spins
I=4 and 6, are eigenstates of any two-body interaction. These states have good
seniority for an arbitrary interaction. In this work an analytic proof is given
to this peculiar occurrence of partial conservation of seniority which is the
consequence of the special property of certain coefficients of fractional
parentage. Further calculations did not reveal its existence in systems with
other $n$ and/or $I$ for shells with $j\leq15/2$.
