Random Uniform Forests are a variant of Breiman's Random Forests (tm) (Breiman, 2001) and Extremely randomized trees (Geurts et al., 2006). Random Uniform Forests are designed for classification, regression and unsupervised learning. They belong to the family of ensemble learning and build many unpruned and randomized binary decision trees then use averaging (regression) or majority vote (classification) to take a decision. Unlike Random Forests, they draw random cut-points, using the continuous Uniform distribution for each node (region) to grow each tree. Unlike Extremely randomized trees, they use bootstrap (only for classification) and subsampling, since Out-of-bag (OOB) modeling plays a key role. Unlike both algorithms, for each node sampling with replacement is done to select features. Random Uniform Forests are aimed to get low correlated trees, to allow a deep analysis of variable importance (Ciss, 2015b) and to be natively distributed and incremental. Random uniform decision trees are the core of the model. We provide an R package, randomUniformForest, and present main theoretical arguments. The algorithm follows and extends Breiman's key idea : increase diversity to build uncorrelated trees. Hence the main motivation of Random Uniform Forests is to be more weakly dependent to the data than Random Forests while giving similar performance and inheriting of all their theoretical properties.