We explain a time complexity reduction algorithm that improves the line spectral frequencies (LSF) search procedure on the unit circle for low bit rate speech codecs. The algorithm is based on strong interframe correlation exhibited by LSFs. The fixed point C code of ITU-T Recommendation G.723.1, which uses the “real root algorithm” was modified and the results were verified on ARM-7TDMI general purpose RISC processor. The algorithm works for all test vectors provided by International Telecommunications Union-Telecommunication (ITU-T) as well as real speech. The average time reduction in the search computation was found to be approximately 20%.