Non-coding RNAs play a major role in diverse processes in living cells with their sequence and spatial structure serving as the principal determinants of their function. Superposition of RNA 3D structures is the most accurate method for comparative analysis of RNA molecules and for inferring sequence alignments. Topology-independent superposition is particularly relevant, as evidenced by structurally similar RNAs with sequence permutations such as tRNA and Y RNA. To date, state-of-the-art methods for RNA 3D structure superposition rely on intricate heuristics, and the potential for topology-independent superposition has not been exhausted. Recently, we introduced the ARTEM method for unrestrained pairwise superposition of RNA 3D modules and now we developed it further to solve the global RNA 3D structure alignment problem. Our new tool ARTEMIS significantly outperforms state-of-the-art tools in both sequentially-ordered and topology-independent RNA 3D structure superposition. Using ARTEMIS we discovered a helical packing motif to be preserved within different backbone topology contexts across various non-coding RNAs, including multiple ribozymes and riboswitches. We anticipate that ARTEMIS will be essential for elucidating the landscape of RNA 3D folds and motifs featuring sequence permutations that thus far remained unexplored due to limitations in previous computational approaches.