In this paper, we analyze the footpoint motion of two large solar flares using observations made by the Transition Region and Coronal Explorer (TRACE) and Reuven Ramaty High Energy Solar Spectroscopic Imager ( RHESSI). The two flares are the M5.7 flare of March 14, 2002 and the X10 flare of October 29, 2003. They are both classical two-ribbon flares as observed in TRACE 1600 or 171 Å images and have long-duration conjugate hard X-ray (HXR) footpoint emission. We use the ‘center-of-mass’ method to locate the centroids of the UV/EUV flare ribbons. The results are: (1) The conjugate UV/EUV ribbons and HXR footpoints of the two flares show a converging (inward) motion during the impulsive phase. For the two flares, the converging motion lasts about 3 and 10 min, respectively. The usual separation (outward) motion for the flare ribbons and footpoints take place only after the converging motion. (2) During the inward and the outward motion, the conjugate ribbons and footpoints of the two events exhibit a strong unshear motion. In obtaining above results, TRACE UV/EUV and RHESSI HXR data show an overall agreement. The two events demonstrate that the magnetic reconnection for the flares occurs in highly sheared magnetic field. Furthermore, the results support the magnetic model constructed by Ji et al. [Ji, H., Huang, G., Wang, H. Astrophys. J. 660, 893–900, 2007], who proposed that the contracting motion of flaring loops is the signature of the relaxation of sheared magnetic fields.