Bayesian network structure learning by recursive autonomy identification. We propose the recursive autonomy identification (RAI) algorithm for constraint-based (CB) Bayesian network structure learning. The RAI algorithm learns the structure by sequential application of conditional independence (CI) tests, edge direction and structure decomposition into autonomous sub-structures. The sequence of operations is performed recursively for each autonomous sub-structure while simultaneously increasing the order of the CI test. While other CB algorithms d-separate structures and then direct the resulted undirected graph, the RAI algorithm combines the two processes from the outset and along the procedure. By this means and due to structure decomposition, learning a structure using RAI requires a smaller number of CI tests of high orders. This reduces the complexity and run-time of the algorithm and increases the accuracy by diminishing the curse-of-dimensionality. When the RAI algorithm learned structures from databases representing synthetic problems, known networks and natural problems, it demonstrated superiority with respect to computational complexity, run-time, structural correctness and classification accuracy over the PC, three phase dependency analysis, optimal reinsertion, greedy search, greedy equivalence search, sparse candidate, and max-min hill-climbing algorithms.