A novel method to measure x-ray-absorption spectra without the inner-shell lifetime broadening is presented. It is based on a high-resolution spectrometer which can be used to analyze the fluorescence photon energy with better resolution than the natural linewidth. The dramatic improvement in resolution and detailed structure for the x-ray-absorption near-edge structure (XANES) at the Dy L(III) edge is presented. This new technique reveals structure which is totally invisible using conventional XANES.