Let \(\mathcal{H}=\mathcal{H}_0\oplus \mathcal{H}_1\) be a separable Hilbert space and consider the \(2\times 2\) operator matrix \(H_0=\left[\begin{smallmatrix} A_0 & T_{01} \\ T_{10} & A_1\end{smallmatrix}\right]\), where \(A_0\) is a (possibly unbounded) selfadjoint operator, bounded from below by some constant \(\alpha_0\in\mathbb{R}\), \(A_1\) is a bounded selfadjoint operator, and the unbounded coupling operators \(T_{01}\) and \(T_{10}\) are subject to the following conditions: (i) \(T_{01}\) is a densely defined closable operator, (ii) \(T_{10}\) is the adjoint operator of \(T_{01}\), that is, \(T_{10}=T_{10}^*\), and \(\mathcal{D}(T_{10})\supset \mathcal{D}(|A_0|)\). Factorizations of the transfer function associated with the self-adjoint \(2\times 2\) operator matrix \(H_0\) are constructed and completeness and basis properties of the eigenvectors of the transfer function corresponding to the real point spectrum of \(H_0\) are proved. Some properties of the root vectors of the analytically continued transfer function are discussed.