A generalized form of the Coles compressibility transformation is utilized to analyze compressible turbulent boundary-layer flows. The generalization in the transformation is distinguished by specifying a stretching parameter that depends upon both space variables rather than on only the streamwise coordinate. This modification is shown to eliminate the distortion observed in the wake region of the transformed velocity profiles. For zero pressure gradient flows, predictions based upon the analysis are consistently superior with predictions due to Spalding-Chi and Baronti-Libby. A wide range of experimental data have been examined with Mach numbers ranging as high as 8, wall to free stream total temperature ratios as low as 0.25 and momentum thickness Reynolds numbers up to approximately one million.