A number of studies on using friction based energy dissipation system for seismic protection of the building have been published in the recent past. The studies show that numerical approximation of the effectiveness of the friction based energy dissipation system depends on the accurate solution of the relevant nonlinear equations of motion. The available numerical models to idealize the behaviour of friction dampers can be categorized into equivalent linearization method, approximation by rigid-perfectly plastic hysteric model and stick-slide condition model. However, it has been observed that the minimum difference in relative velocity or non-identification of exact time of phase transition from stick to slide condition results in a noticeably high fluctuation of relative velocity in the stick-slide model. To identify the exact time for phase transition, this paper presents a numerical methodology for dynamic analysis of buildings with friction damper, leading to improved accuracy of solutions of equations of motion. The mathematical formulation and solution procedure of the proposed methodology has been presented in detail in this paper. The results obtained have been validated with examples from published literature. The response of single degree of freedom (SDOF) system with friction device when subjected to nine different ground motions are presented. The selected ground motion encompasses three ground motions each from soft soil, medium soil and hard soil to evaluate the likely response of the structure under the likely range of expected ground motion characteristics. The spectral variation with reference to pretension force has been investigated and presented. The results indicate that for a particular range of pretension force, beyond a particular stiffness ratio, the reduction in spectral response of the damper added system is independent of frequency of the SDOF system, which shows the robustness of friction devices.