In this article, we study the formation of the bound states in the continuum (BICs) in a two-channel Fano-Anderson model. We employ the Green's function formalism, together with the equation of motion method, to analyze the relevant observables, such as the transmission coefficient and the density of states. Most importantly, our results show that the system hosts true BICs for the case of a symmetric configuration with degenerate impurity levels, and a complete transmission channel is then suppressed. Finally, we argue that the proposed mechanism could be relevant for the realization of BICs in electronic and photonic systems.