There is no universal definition of stability for RNA secondary structures. Here we present an approach that is based on normalization of the equilibrium free energy to the length of the sequence: a segment of RNA is said to be stable if the ratio of the equilibrium free energy to the length of the segment is greater than a certain threshold value. Discarding the segments whose normalized equilibrium free energies are smaller than the threshold allows us to view the secondary structure at different levels of stability. Confined to only highly stable structures, the algorithm for secondary structure prediction admits a number of simplifications that make it computationally tractable for large sequences and advantageous over most other methods on a genome-wide scale. This method was applied to the Caenorhabditis elegans genome to localize the regions that encode stable secondary structures. In particular, 36 of 56 previously reported micro-RNAs were localized to 4% of the genome. A fraction of long (>or=400 nt) stable inverted repeats in the genomic sequence of C.elegans was found. Their distribution is very uneven, and skewed towards the ends of chromosomes. This method can be used for genome-wide detection of transcription termination signals, putative micro-RNAs, and other regulatory elements that involve stable RNA secondary structures.