The universal semi-empirical equation has been commonly used to quantitatively describe the energy dependence of the secondary electron yield (SEY). It is even used as a first reliability test for experimental data. The equation is based on the assumption that the stopping power is constant along the electron trajectory. In this article, we derive a novel analytical expression based on a more advanced model which considers linear stopping power dependence on penetration depth. Although coinciding with the universal equation at low energies, the novel function has lower intensity in the higher energy range. The models were compared with experimental SEY data of different metals, taken from literature, as well as freshly cleaved highly oriented pyrolytic graphite, measured in the frame of this work. It is confirmed that the novel expression better describes the experimental data.