XAFS (X-ray absorption fine-structure) spectra were measured near K-absorption edges of Ce (40.5 keV), Dy (53.8 keV), Ta (67.4 keV) and Pt (78.4 keV). The blunt K-edge jump due to the finite lifetime of the core hole was observed. This makes it difficult to extract EXAFS (extended X-ray absorption fine-structure) functions at low k values. Local structure parameters can be evaluated from the EXAFS spectra above K-absorption edges in the high-energy region as well as from those above L(III)-edges. It was found that the finite-lifetime effect of the core hole is effectively taken into the photoelectron mean-free-path term, as predicted theoretically.