By use of the shadow theory developed recently, this paper deals with the transverse electric (TE) wave diffraction by a perfectly conductive periodic array of rectangular grooves. A set of equations for scattering factors and mode factors are derived and solved numerically. In terms of the scattering factors, diffraction amplitudes and diffraction efficiencies are calculated and shown in figures. It is demonstrated that diffraction efficiencies become discontinuous at an incident wave number where the incident wave is switched from a propagating wave to an evanescent one, whereas scattering factors and diffraction amplitudes are continuous even at such an incident wave number.