The integrated external bremsstrahlung (EB) produced by beta particles from 90Sr-90Y, 90Y, 32P and 89Sr sources in different thicknesses of Cu, Ag, Cd, Sn and Pb targets, is measured with a NaI(Tl) scintillation spectrometer. The external bremsstrahlung intensity increases rapidly with target thickness, but the increase of the intensity is not linear. This nonlinear increase of EB intensity is shown to follow an empirical relation of the type t exp(- Sigma Bt), where t is the thickness of the target in mg cm-2 and Sigma B is a constant. Sigma B(cm2mg-1) is found to be a constant and independent of the atomic number of the target. Sigma B is determined for 90Sr-90Y, 90Y, 32P and 89Sr beta sources. The values of Sigma B are found to be constant and agree with each other within 15-20% for these beta sources, showing that Sigma B is constant, independent of the atomic number of the target and also independent of the end-point energy of the beta spectrum.