  A new set of polynomial states (to be called character states) are derived
for $Sp(4)$ reduced to its $SU(2) \times U(1)$ subgroup, and the relevant
generator matrix elements are evaluated for generic representations $(a,b)$ of
$Sp(4)$. (The degenerate representations $(a,0)$ and $(0,b)$ were treated in
our previous work and are also given in this paper). The group--subgroup in
question is that of the seniority model of nuclear physics.
