  We study the distribution of Hasse's unit index $Q(L)$ for the CM-fields $L =
\mathbb{Q}(\sqrt{d}, \sqrt{-1})$ as $d$ varies among positive squarefree
integers. We prove that the number of $d\leq X$ such that $Q(L) = 2$ is
proportional to $X/\sqrt{\log X}$.
