Iran, among the world most earthquake-prone countries, has been exposed to the devastating earthquake in the past years and it is inevitable to find strategy for confronting with this phenomenon. In this regard, eccentrically diagonal bracing as a lateral system has been of less interest to the researchers and design engineers. To promote use of the system, in this study the cyclic behavior of steel frames with eccentrically diagonal bracing in two cases of simple and rigid beam to column connections are compared and the advantage of rigid connection in better drift control due to too much flexibility in simple connection has been investigated in two cases with high and low eccentricities. Close results (difference between link beam shear force and also axial forces in braces and columns of about 20%) of two cases in small eccentricity make it possible for engineers to get rid of the problems in rigidity achievement in Iran with full penetration welds. Moreover by increasing eccentricity, the behavior of the link beam would change from shear to moment link, reducing energy dissipation in the system. However, using rigid connection can increase energy dissipation up to 50%. The use of rigid connections in such frames with larger eccentricities decrease compressive stress about 12% and prevent buckling of braces compared to the case with simple connection.