This paper is dedicated to the following Choquard system: \(\begin{aligned} {\left\{ \begin{array}{ll} -\Delta u + u = \frac{2p}{p+q} \left( I_\alpha * |v|^q\right) |u|^{p-2} u, \quad \text {in } \mathbb {R}^N, \\ -\Delta v + v = \frac{2q}{p+q} \left( I_\alpha * |u|^p\right) |v|^{q-2} v, \quad \text {in } \mathbb {R}^N. \\ \end{array}\right. } \end{aligned}\) where \(N \ge 4\) , \(I_\alpha \) is a Riesz potential of order \(\alpha \in (N-4, N)\) and \(2< p, q < \frac{N+\alpha }{N-2}\) with \(p\ne q\) . By the minimax method on the Nehari manifold, for any given \(1\le k\le N\) , we construct a minimal action \(k-odd\) solution with exactly \(2^{k}\) nodal domains of the Choquard system. This is a new phenomenon for the Choquard system which is nonlocal in nature when compared with its local counterpart the nonlinear Schrödinger system.
