A sample of 25 QSOs is used to investigate the average spectrum between the soft X-ray energy band of the Einstein Observatory Image Proportional Counter, and the higher energy band of the HEAO 1 A-2 experiment. Assuming a power-law spectrum, a 90 percent confidence range is found for alpha(F(v) approximately v to the -alpha of 0.83 (+0.32, -0.22) for N(H) lower than 3 x 10 to the 20th atoms/sq cm. Higher column densities for QSOs are not anticipated, but if N(H) were about 10 to the 22nd atoms/sq cm, then alpha would be greater then 0.97. The present spectrum is similar to those exhibited by Seyfert galaxies and narrow emission line galaxies above 2 keV. The spectrum is soft enough that, if these objects are typical of the higher redshift, more radio-quiet QSOs, then QSOs can be excluded as being the dominant origin of the diffuse X-ray background.