algebraic number theory - Relative integral basis for CM extensions

Suppose $K=mathbf{Q}(sqrt{d})$; it's well known that $mathcal{O}_K$ is $mathbf{Z}+frac{D+sqrt{D}}{2}mathbf{Z}$, where $D$ is the discriminant.

What is the analogue of this for a CM extension $F(sqrt{-alpha})/F$, where $F$ is totally real (of class number one) and $alpha in mathcal{O}_F$ is totally positive?

Is there a canonical element $xi$ of $F(sqrt{-alpha})$ such that $mathcal{O}_{F(sqrt{-alpha})}=mathcal{O}_F+xi mathcal{O}_F$?

I have looked in the literature, but all I can find are various theorems guaranteeing the nonexistence of relative integral bases in various situations. However a theorem in Chapter 7 of Narkiewicz's book guarantees that some $xi$ does exist in the above situation.