We report a detailed examination of the fine structure inside flare ribbons and the temporal evolution of such structure during an X2.3 solar flare, which occurred on 2001 April 10. We examined fine structures, such as systems of conjugate footpoints, inside flare ribbons by using the Hα images obtained with the Sartorius telescope at Kwasan Observatory, Kyoto University. We identified the conjugate footpoints of each Hα kernel in both flare ribbons by a new method that uses cross-correlation functions of the light curves. We also compared the sites of the Hα kernels with the spatial configurations of flare loops seen in the extreme-ultraviolet images obtained with the Transition Region and Coronal Explorer. We found that the highly correlated pairs of Hα kernels were connected by flare loops seen in the 171 Å images. Investigating such fine structures inside the flare ribbons, we can follow the history of energy release and perhaps acquire key information about particle acceleration.