This paper deals with the following nonlinear elliptic equation$$-\Delta u=Q(|y'|,y'')u^{\frac{N+2}{N-2}},,,u>0,,,\text{in}\R^N,,,u\inD^{1,2}(\R^{N}),$$where $(y',y'')\in \R^2\times\R^{N-2}$,$Q(|y'|,y'')$ is a bounded non-negative function in$\mathbb{R}^{2}\times \R^{N-2}$. We prove a non-degeneracy result for the positive multi-bubbling solutions constructed in\cite{PWW}.