The beam-to-column connections in most steel frames are assumed to be pinned or rigid. All structural connections have some specified values of flexibility under the loading. In this paper, the effect of flexibility of connections in buckling analyses of a plane steel frame is investigated. Accordingly, end-fixity factor used for taking into account the pinned, rigid, semi-rigid, and khorjini connections in the analyses. Furthermore, new technique for analysis of steel frames with khorjini joints is proposed. Based on the presented approach, all analytic equations of semi-rigid frames are developed for analysis of khorjin frames. In order to verify the presented method, several numerical examples are solved. Moreover, the stiffness matrix of a beam-column element, which can take into account the second-order effects and flexibility of connections, is derived. This matrix is very general and can be applied to a frame member with any type of connection. The new formula is more accurate and efficient than the corresponding matrices obtained by other authors. By assembling the stiffness matrix of frame and calculating the minimum positive eigenvalue of this matrix, buckling load of the frame is obtained. To demonstrate the validity and efficiency of proposed approach, several numerical examples are solved. Results show that the response of khorjini frame is close to the one with the semi-rigid joints. The buckling loads of the steel frame with khorjini connections are close to the one with the semi-rigid joints.