In a one-color spectrum of threshold electrons produced in pulsed ionization of long-lived (0.1-1.0 mu s) Rydberg states of naphthalene by an electric field, a new group of electrons was observed. It was attributed to the two-step excitation of high-lying Rydberg states of a molecule, which converge to the first excited electronic state of a cation. A refined value of the second adiabatic ionization energy of naphthalene was obtained (8.913 +/- 0.004 eV).