Random Forests have been shown to perform very well in propositional learning. FORF is an upgrade of Random Forests for relational data. In this paper we investigate shortcomings of FORF and propose an alternative algorithm, R⁴F, for generating Random Forests over relational data. R⁴F employs randomly generated relational rules as fully self-contained Boolean tests inside each node in a tree and thus can be viewed as an instance of dynamic propositionalization. The implementation of R⁴F allows for the simultaneous or parallel growth of all the branches of all the trees in the ensemble in an efficient shared, but still single-threaded way. Experiments favorably compare R⁴F to both FORF and the combination of static propositionalization together with standard Random Forests. Various strategies for tree initialization and splitting of nodes, as well as resulting ensemble size, diversity, and computational complexity of R⁴F are also investigated.