This article proposes a novel Bayesian nonparametric model for relational data. The model exploits a connection between rectangular partitioning models and Baxter permutations to introduce a new class of rectangular partitioning process, called Baxter permutation processes. As mentioned by the reviewers, this paper is creative and brings a new perspective on such class of models. The properties of the model are well described, and the proposed approach compared to suitable baselines.