RNA structures possess multiple levels of structural organization. Secondary structures are made of canonical (i.e. Watson-Crick and Wobble) helices, connected by loops whose local conformations are critical determinants of global 3D architectures. Such local 3D structures consist of conserved sets of non-canonical base pairs, called RNA modules. Their prediction from sequence data is thus a milestone toward 3D structure modelling. Unfortunately, the computational efficiency and scope of the current 3D module identification methods are too limited yet to benefit from all the knowledge accumulated in modules databases. Here, we introduce BayesPairing 2, a new sequence search algorithm leveraging secondary structure tree decomposition which allows to reduce the computational complexity and improve predictions on new sequences. We benchmarked our methods on 75 modules and 6360 RNA sequences, and report accuracies that are comparable to the state of the art, with considerable running time improvements. When identifying 200 modules on a single sequence, BayesPairing 2 is over 100 times faster than its previous version, opening new doors for genome-wide applications.