As was pointed out to the author by E. Benjamin, the proof of Theorem 1 is incomplete. The argument in the penultimate sentence in that proof fails to take into account, for example, the case \begin{gather*} p_1\equiv 3\;{\rm mod}\;4,\;\;p_j\equiv 1\;{\rm mod}\;4 \qquad (j\geq 2),\\ \left(\f{p_i}{p_j}\right)=\begin{cases} +1 & \quad \text{if }\;i=1,\;j\neq i\\ -1 & \quad \text{if }\; i>1,\;j\neq i.\end{cases} \end{gather*} A treatment of some, but not all, missing cases can be found in a preprint by Benjamin (``On Imaginary Quadratic Number Fields with 2-Class Group of Rank 4 and infinite 2-Class Field Tower,'' 1999). We describe here a revision of the original argument which treats all cases simultaneously, thus completing the proof of Theorem 1.