The classical RNA secondary structure model considers A.U and G.C Watson-Crick as well as G.U wobble base pairs. Here we substitute it for a new one, in which sets of nucleotide cyclic motifs define RNA structures. This model allows us to unify all base pairing energetic contributions in an effective scoring function to tackle the problem of RNA folding. We show how pipelining two computer algorithms based on nucleotide cyclic motifs, MC-Fold and MC-Sym, reproduces a series of experimentally determined RNA three-dimensional structures from the sequence. This demonstrates how crucial the consideration of all base-pairing interactions is in filling the gap between sequence and structure. We use the pipeline to define rules of precursor microRNA folding in double helices, despite the presence of a number of presumed mismatches and bulges, and to propose a new model of the human immunodeficiency virus-1 -1 frame-shifting element.