The first experimental observation of the annihilation process of wedge disclinations through a certain special configuration between a pair of wedge disclinations with s = ± in the nematic P-4-BCMU lyotropic liquid crystal phase is reported in this communication. Our results indicate that besides the transitional motion, a rotation of disclinations with s = ± occurs in the liquid crystal phase, leading to the formation of a certain special configuration shortly before annihilation. The rotation of disclinations is explained qualitatively by the elastic anisotropy of the liquid crystals.