Summary: ``In this paper, we study the unconditional uniqueness of solution for the Cauchy problem of $\dot H^{s_c}$ $(0\leq s_c<1)$ critical nonlinear Schrödinger equations (NLS). By employing paraproduct estimates and Strichartz estimates, we prove that unconditional uniqueness of solution holds in $C_t(I;\dot H^{s_c}({\Bbb R}^d))$ for $d\geq 6$. This extends earlier results by Yin Yin Su Win and Y. Tsutsumi [19] [MR2474179] and Cazenave [3] [MR2002047].''