Abstract: The fundamental matrix’s expression is usually F=K -T ×RK -1 , where K is the intrinsic parameters matrix of camera,and R and t is the rotation matrix and the translation vector of camera respectively. The expression is not valid when using the pure rotation. In the paper here, a new expression of the fundamental matrix , F= ×KRK -1 , is presented, where e′ is epipolar point.Net only the expression is valid when using the pure rotation, but also it predigestes the following problems, such as, the intrinsic parameters matrix, the motion parameters, and structure recovery from uncalibrated stereo rig.