The atmosphere protects humans, plants, animals, and microorganisms from damaging doses of ultraviolet-B (UVB) solar radiation (280-320 nm) because it modifies the UVB reaching the Earth's surface. This modification is a function of the solar radiation's path length through the atmosphere and the amount of each attenuator along the path length. The path length is determined by solar zenith angle (SZA). The present work explains the dependence of hemispherical transmittance of UVB on SZA. The database used consists of five years of hourly UVB and global solar radiation measurements. From 2001 to 2005, the South Valley University (SVU) meteorological research station (26.20 degrees N, 32.75 degrees E) carried out these measurements on a horizontal surface. In addition, the corresponding extraterrestrial UVB (UVBext) and broadband solar radiation (G(ext)) were estimated. Consequently, the hemispherical transmittance of UVB (K-tUVB) and the hemispherical transmittance of global solar radiation (K-t) were estimated. Furthermore, the UVB redaction due to the atmosphere was evaluated. An analysis of the dependence between KtUVB and SZA at different ranges of K-t was performed. A functional dependence between K-tUVB and SZA (K-tUVB=-a(SZA)+b) for very narrow Kt-ranges (width of ranges was 0.01) was developed. The results are discussed, and the sensitivity of Delta K-tUVB to Delta SZA for very narrow Kt-ranges was studied. It was found that the sensitivity of Delta K-tUVB to Delta SZA slightly increases with increased K-t, which means K-tUVB is sensitive to SZA as K-t increases. The maximum correlation (R) between K-tUVB and SZA was equal to -0.83 for K-t = 0.76.