Damping through friction tends to be one of the most efficient methods to suppress damage to structures from earthquakes. Realizing robust structures is therefore highly dependent on designing for the dynamic forces of friction- damped structures and exploring their reliability against natural disasters. This paper presents a simplified matrix analysis algorithm for multi-storey friction- damped buildings. We have analyzed the behavior of friction- damped systems more accurately by modeling the master-slave degree of freedom of the joints. First, the formulation of the problem is discussed, and a condensed general equation is derived. Then, an end- to- end solution is proposed to find the responses of structures. The displacement response of each storey has been carried out in both condensed and non-condensed general equations, and the results clearly show the accuracy of the proposed method. The numerical analysis and the results of the simulation of various friction- damped structures depicts the proposed approach consists with the commercial finite element method and is applicable for the analysis various types of structures. It is noted that the acceleration and displacement responses of the structures investigated under the proposed method and the traditional finite element method are so consistent that only a 1.5% difference is observed. Moreover, as a result of the proper allocation of degrees of freedom during the analysis, this method yields a reduction in computational costs especially in large buildings.