We describe in this paper a new method for measuring the K shell photoelectric cross sections of high-Z elemental targets at a K absorption edge. In this method the external bremsstrahlung (EB) photons produced in the Ni target foil by beta particles from a weak[superscript 90]Sr-[superscript 90]Y beta source are passed through an elemental target and the spectrum of transmitted EB photons is measured with a HPGe detector coupled to a 2K ORTEC multichannel analyser spectrometer. The measured spectrum shows a sharp decrease in transmitted intensity at the K absorption edge of the element. Such a sharp decrease is used to determine the K shell photoelectric cross section at the K edge as well as the K absorption edge of the element. We report the data for Gd, Hf, Ta, Au and Pb targets. (Contains 1 footnote, 1 table, and 5 figures.)