Summary: We investigate the spectral singularities and the eigenvalues of the boundary value problem \[ \begin{gathered} y'' + \big[\lambda -Q(x)\big]^{2}y=0, \quad x\in \mathbb R_{+}= [0,\infty), \\ \int\limits_{0}^{\infty} K(x)y(x)\, dx+\alpha y' (0)-\beta y(0)=0, \end{gathered} \] where \(Q\) and \(K\) are complex valued functions, \(K\in L^2(\mathbb R_+)\), \(\alpha,\beta\in \mathbb C\) with \(|\alpha|+|\beta|\neq 0\) and \(\lambda\) is a spectral parameter.