A ribonucleic acid (RNA) is one of the two types of nucleic acids found in living organisms. An RNA molecule represents a long chain of monomers called nucleotides. The sequence of nucleotides of an RNA molecule constitutes its primary structure, and the pattern of pairing between nucleotides determines the secondary structure of an RNA. Non-coding RNA genes produce transcripts that exert their function without ever producing proteins. Predicting the secondary structure of non-coding RNAs is very important for understanding their functions. We focus on Nussinov’s algorithm as useful techniques for predicting RNA secondary structures. We introduce a new traceback matrix and scoring table to improve above algorithm. And the improved prediction algorithm provides better levels of performance than the originals.