The Rfam database contains information about non-coding RNAs emphasizing their secondary structures and organizing them into families of homologous RNA genes or functional RNA elements. Recently, a higher order organization of Rfam in terms of the so-called clans was proposed along with its "decimal release". In this proposition, some of the families have been assigned to clans based on experimental and computational data in order to find related families. In the present work we investigate an alternative classification for the RNA families based on tree edit distance. The resulting clustering recovers some of the Rfam clans. The majority of clans, however, are not recovered by the structural clustering. Instead, they get dispersed into larger clusters, which correspond roughly to well-described RNA classes such as snoRNAs, miRNAs, and CRISPRs. In conclusion, a structure-based clustering can contribute to the elucidation of the relationships among the Rfam families beyond the realm of clans and classes.