  Let $O$ be an order of odd discriminant $D$ in an imaginary quadratic field
$K$. Let $Cl(O)$ be the group of proper $O$-ideals and $Cl(O)[2]$ the kernel of
multiplication by $2$ in $Cl(O)$. We describe explicitly the group $Cl(O)[2]$.
In particular, we prove that its order is
  $2^{s_D-1}$ where $s_D$ is the number of prime divisors of $D$.
