The dust reddening law from the UV to the near-IR for the extended regions of galaxies is here derived from the spectral distributions of the starburst spiral galaxies NGC 7552 and NGC 5236. The centers of these galaxies have similar absorption and emission line spectra, differing only if the strength of their interstellar lines and in the continuum distribution, with NGC 7552 appearing more reddened than NGC 5236. The disk of NGC 7552 is more inclined, and there is evidence that its center is observed through additional foreground dust and gas clouds, as compared to the center of NGC 5236. While the galaxies can be expected to have similar dust content, they are known to have different dust path lengths to our line of sight. Therefore, differences in the shape of the spectra can be attributed mainly to the effects of dust, allowing us to probe for the first time the properties of the reddening law outside the local group of galaxies. We derive the reddening law based on the optical depth of the emission line of H Alpha and H Beta and also based on the continuum distribtuion. We find that the optical depth from the emission line regions are about twice the optical depth of the continuum regions. Thus, dereddening a starburst galaxy by scaling the Milky Way reddening laws to optical depths obtained from the H Alpha/H Beta line ratio overcompensates for the effect of dust.