A new accurate finite-difference time-domain model of dielectric and conductive layers on metal surfaces is developed. The model is based on higher-order surface impedance boundary conditions (SIBC). Several improvements to the existing numerical SIBC models are presented. The most important features of the proposed model are the inclusion of the tangential variations of the fields into the model and a considerably more accurate approximation of the impedance function than in the earlier works. In addition to the usual dielectric and conductive layers, the model can also handle layers of Lorentz, Debye, or Drude media. It is shown that the range of applicability of the proposed SIBC model is greatly increased as compared with the earlier models. Verification of the model is performed with one- and two-dimensional simulations. The results are compared with the exact results in both time and frequency domains. Also, a comparison with an earlier model is provided.