The corotational frame method is widely used in the simulation of flexible multibody dynamics. Its core idea is to separate the rigid motion from the flexible deformation so that it can make fully exploit a large number of excellent local finite elements. The essence of the conventional corotational frame method is the projection relationship between the element frame and the global frame. This paper explores another coordinate projection method for two-dimensional (2D) corotational beam element. The projection relationship between the element frame and the local frame in the framework of Lie algebra has been proposed. Based on the description of , the formulation of corotational beam element and integration algorithm is presented. The local frame description greatly reduces the nonlinearity of the formula by eliminating the effect of the rigid body motion on the projection matrix, internal force and inertial force. Several examples of large deformation and large rotation are performed, and it is found that the step-size convergence and iterative efficiency of description are improved compared with description. Moreover, some examples are used given to verify that the frame invariance brought by is valuable for improving computing efficiency. The presented transformation method can easily extend to other 2D elements.