It has been an accepted fact for more than 40 years that the E center in Si (the group-V impurity--vacancy pair)--one of the most studied defects in semiconductors--has only one energy level in the band gap: namely, the acceptor level at about 0.45 eV below the conduction band. We now demonstrate that it has a second level, situated in the lower half of the band gap at 0.27 eV above the valence band. The existence of this level, having a donor character, is disclosed by a combination of different transient-capacitance techniques and electronic-structure calculations. The finding seriously questions some diffusion-modeling approaches performed in the past.