Background Structural alignment of RNAs is becoming important, since the discovery of functional non-coding RNAs (ncRNAs). Recent studies, mainly based on various approximations of the Sankoff algorithm, have resulted in considerable improvement in the accuracy of pairwise structural alignment. In contrast, for the cases with more than two sequences, the practical merit of structural alignment remains unclear as compared to traditional sequence-based methods, although the importance of multiple structural alignment is widely recognized. Results We took a different approach from a straightforward extension of the Sankoff algorithm to the multiple alignments from the viewpoints of accuracy and time complexity. As a new option of the MAFFT alignment program, we developed a multiple RNA alignment framework, X-INS-i, which builds a multiple alignment with an iterative method incorporating structural information through two components: (1) pairwise structural alignments by an external pairwise alignment method such as SCARNA or LaRA and (2) a new objective function, Four-way Consistency, derived from the base-pairing probability of every sub-aligned group at every multiple alignment stage. Conclusion The BRAliBASE benchmark showed that X-INS-i outperforms other methods currently available in the sum-of-pairs score (SPS) criterion. As a basis for predicting common secondary structure, the accuracy of the present method is comparable to or rather higher than those of the current leading methods such as RNA Sampler. The X-INS-i framework can be used for building a multiple RNA alignment from any combination of algorithms for pairwise RNA alignment and base-pairing probability. The source code is available at the webpage found in the Availability and requirements section.