Recently, a large number of candidates of non-coding RNAs (ncRNAs) has been predicted by experimental or computational approaches. Moreover, in genomic sequences, there are still many interesting regions whose functions are unknown (e.g., indel conserved regions, human accelerated regions, ultraconserved elements and transposon free regions) and some of those regions may be ncRNAs. On the other hand, it is known that many ncRNAs have characteristic secondary structures which are strongly related to their functions. Therefore, detecting clusters which have mutually similar secondary structures is important for revealing new ncRNA families. In this paper, we describe a novel method, called RNAclique, which is able to search for clusters containing mutually similar and locally stable secondary structures among a large number of unaligned RNA sequences. Our problem is formulated as a constraint quasi-clique search problem, and we use an approximate combinatorial optimization method, called GRASP, for solving the problem. Several computational experiments show that our method is useful and scalable for detecting ncRNA families from large sequences. We also present two examples of large scale sequence analysis using RNAclique.