The excitation spectrum of the L3M5 X-ray emission of Dy3+ system in the pre-edge region of Dy L3 XANES is theoretically investigated based upon a coherent second order optical formula with multiplet coupling effect. The spectral broadening of the excitation spectrum is determined by the M5, core hole lifetime, being free from the L3 core hole lifetime. The fine pre-edge structure of L3 edge due to L3N6,7 quadrupole transition can be seen in the excitation spectrum, while this structure is invisible in the conventional XANES. The conditions for the excitation spectrum to be regarded as the absorption spectrum with a smaller width are discussed.