In this paper we present a method to compute similarities on unlabeled data, based on extremely randomized trees. The main idea of our method, Unsupervised Extremely Randomized Trees (UET) is to randomly split the data in an iterative fashion until a stopping criterion is met, and to compute a similarity based on the co-occurrence of samples in the leaves of each generated tree. We evaluate our method on synthetic and real-world datasets by comparing the mean similarities between samples with the same label and the mean similarities between samples with different labels. Our empirical study shows that the method effectively gives distinct similarity values between samples belonging to different clusters, and gives indiscernible values when there is no cluster structure. We also assess some interesting properties such as invariance under monotone transformations of variables and robustness to correlated variables and noise. Finally, we performed hierarchical agglomerative clustering on synthetic and real-world homogeneous and heterogeneous datasets using UET. Our experiments show that the algorithm outperforms existing methods in some cases, and can reduce the amount of preprocessing needed with many real-world datasets.