For ordinals \(\alpha\), \(\beta\), \(\gamma_0\), \(\gamma_1\), \(\delta_0\), and \(\delta_1\), the balanced polarized partition relation
\[ \left(\begin{matrix} \alpha\\ \beta \end{matrix}\right) \rightarrow \left(\begin{matrix} \gamma_0 & \gamma_1\\ \delta_0 & \delta_1 \end{matrix}\right)^{1,1} \]
holds if for any partition of \(\beta\times\alpha=K_0\cup K_1\) into two classes, either there are \(D_0\in [\beta]^{\delta_0}\) and \(C_0\in [\alpha]^{\gamma_0}\) with \(D_0\times C_0\subseteq K_0\), or there are \(D_1\in [\beta]^{\delta_1}\) and \(C_1\in [\alpha]^{\gamma_1}\) with \(D_1\times C_1\subseteq K_1\). In the paper under review it is shown that if \(\text{cf}\kappa=\omega\) and \(\lambda=2^{<\kappa}\), then
\[ \left(\begin{matrix} \lambda^+\\ \lambda \end{matrix}\right) \rightarrow \left(\begin{matrix} \lambda^+ & \alpha\\ \lambda & \kappa \end{matrix}\right)^{1,1} \] for all \(\alpha<\omega_1\).