Given a \(G\)-Brownian motion \(B\) defined over a sublinear expectation space \((\Omega,{\mathcal H},E)\) with a sublinear expectation \(E\) associated with the nonlinear heat equation \(\partial_t u-G(D_x^2u)=0\) in \((0,T]\times \mathbb R^d\), where \(G(A)=\sup_{\gamma\in\Theta}\{\frac{1}{2}\text{tr} (\gamma\gamma^*A)\}\), \(A\in {\mathcal S}^d\) (symmetric matrices in \(\mathbb R^{d\times d}\)) (see [S. Peng, in: Stochastic analysis and applications. The Abel symposium 2005. Proceedings of the second Abel symposium, Oslo, 2005. Berlin: Springer. 541–567 (2007; Zbl 1131.60057); Stochastic Processes Appl. 118, No. 12, 2223–2253 (2008; Zbl 1158.60023)]), the author studies the Girsanov \(\widehat{B}_t:=B_t-\int_0^t(d\langle B\rangle_sh_s)\), \(t\in[0,T]\). (Recall that the quadratic variation process \(\langle B\rangle\) of a \(G\)-Brownian motion \(B\) is a stochastic process, not a deterministic). He shows that, if \(G\) is strictly elliptic, i.e., for some \(\sigma_0>0\), \(\gamma\gamma^*\geq \sigma_0 I_{\mathbb R^d}\), for all \(\gamma\in \Theta\), and if the Doléan-Dade exponential \(D_t=\exp\{\int_0^t h_sdB_s-\frac{1}{2}\int_0^t h_s(d\langle B\rangle_sh_s)\}\) forms a symmetric \(G\)-martingale, then, under \(\widehat{\operatorname{E}}[\, .\,]:=\operatorname{E}[\, . \times D_T]\), the process \(\widehat{B}\) is a \(G\)-Brownian motion. In the author’s approach a characterisation of symmetric \(G\)-martingales using results of L. Denis et al. [Potential Anal. 34, No. 2, 139–161 (2011; Zbl 1225.60057)], plays a central role. The author’s result generalises that by J. Xu et al. [Stochastic Anal. Appl. 29, No. 3, 386–406 (2011; Zbl 1225.60115)], who obtained only a result for 1-dimensional \(G\)-Brownian motions.