Respiratory complex I catalyzes two-electron/two-proton reduction of a ubiquinone (Q) substrate bound at its Q-binding pocket; upon reduction, ubiquinole carries electrons further down the electron transport chain. The mechanism of this two-electron transfer reaction is poorly understood. Here we consider a hypothetical scheme in which two electrons transfer together with two protons in a concerted fashion. On one side, a coupled electron/proton transfer occurs from the reduced N2 FeS cluster and protonated His38 residue, respectively, while on the other side a hydrogen atom transfer occurs from the neutral Tyr87 residue, generating a tyrosyl radical. A method to evaluate the coupling matrix element that corresponds to a concerted tunneling of two electrons was developed. Overall, our calculations indicate that the concerted reaction is feasible, in which case a transient tyrosyl radical is formed during the catalytic cycle of the enzyme.