For a sequence \(\{M_n\}_{n=1}^{\infty}\) of expanding matrices with \(M_n\in M_d(\mathbb{Z})\) and a sequence \(\{D_n\}_{n=1}^{\infty}\) of finite digit sets with \(D_n\subset\mathbb{Z}^{d}\), the Moran measure \(\mu_{\{M_{n}\},\{D_{n}\}}\) is defined by the infinite convolution \[ \mu_{\{M_n\},\{D_n\}}=\delta_{M_{1}^{-1}D_1}\ast\delta_{M_{1}^{-1}M_{2}^{-1}D_2}\ast\delta_{M_{1}^{-1}M_{2}^{-1} M_{3}^{-1}D_3}\ast\cdots \] and the convergence is in the weak sense. Under some additional assumptions, the authors show that \(L^{2}(\mu_{\{M_n\},\{D_n\}})\) contains an infinite orthogonal set of exponential functions if and only if there exists an infinite subsequence \(\{n_{k}\}_{k=1}^{\infty}\) of \(\{n\}_{n=1}^{\infty}\) such that \[ \left(M_{n_{k}+1}^{*}M_{n_{k}+2}^{*}\cdots M_{n_{k+1}}^{*}Z_{n_{k+1}}\right)\cap\mathbb{Z}^{d} \neq \emptyset \] for any \(k\in \mathbb{N}^{+}\), where \(Z_{n_{k+1}}:=\{x: \sum_{\alpha\in D_{n_{k+1}}}e^{2\pi i\langle \alpha,x \rangle}=0\}\cap[0,1)^d\). This extends the results of J. Li [Sci. China, Math. 58, No. 12, 2541–2548 (2015; Zbl 1342.28018)].