In this paper, the authors study the decay of eigenfunctions of the non-self-adjoint matrix operator \(\mathcal{H}=\left( \begin{matrix} -\Delta +\mu+U & W \\ -W & -\Delta -\mu-U \\ \end{matrix} \right)\), for \(\mu>0\), corresponding to eigenvalues \(E\) in the strip \(-\mu<\text{Re}(E)<\mu\). The main result in this paper is Theorem 1.2, which improves the exponential decay estimates due to I. Rodnianski et al. [Dispersive analysis of the charge transfer models, arXiv:math/0309112].