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RNA secondary structure plays the scaffolding role for RNA tertiary conformation. Accurate secondary structure prediction can not only identify double-stranded helices and single stranded-loops but also help provide information for potential tertiary interaction motifs critical to the 3D conformation. The average accuracy in ab initio prediction remains 70%; performance improvement has only been limited to short RNA sequences. Due to intrinsic nucleotide interactions, prediction of tertiary interaction motifs is difficult without multiple, related sequences that are usually not available. This paper presents research that aims to improve the secondary structure prediction performance and to develop a capability to predict coaxial stacking between helices. Coaxial stacking positions two helices on the same axis, a tertiary motif present in almost all junctions that account for a high percentage of RNA tertiary structures. This research identified energetic rules for coaxial stacks and geometric constraints on stack combinations, which were applied to developing an efficient dynamic programming application for simultaneous prediction of secondary structure and coaxial stacking. Results on a number of non-coding RNA data sets, of short and moderately long lengths, show a performance improvement for secondary structure prediction when compared with existing methods. The program also demonstrates a capability for coaxial stacking prediction.