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For a fixed light-heavy pairing, imposing $m_iU_{\\alpha i}U_{\\beta i}+M_iR_{\\alpha i}R_{\\beta i}=0$ together with $UU^\\dagger+RR^\\dagger=\\mathbf{1}$ yields the general exact solution $U=VD^{-1/2}$ and $R=iVE\\,\\operatorname{diag}\\!\\left(\\sqrt{r_i/(1+r_i)}\\right)$, where $r_i=m_i/M_i$, $D=\\operatorname{diag}(1+r_i)$, $V$ is unitary, and $E=\\operatorname{diag}(\\eta_i)$ with $\\eta_i=\\pm1$. 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