  Let $F$ be a field of odd characteristic, $E$ be a finite extension of $F$
equipped an involution with subfield of fixed points $E_0$ containing $F$ and
$V$ be a finite dimensional $E$-vector space with a non-degenerate hermitian
form $h$. We show a link between the spinor norm in the unitary group $U(V,h)$
and the calculus of determinants and discriminants. Then we show a formula
which links the spinor norm in $U(V,h)$ and the spinor norm in the orthogonal
group $O(V,b_h)$ defined by a non-degenerate symmetric bilinear form $b_h$
associated to $h$.
