In this letter, a new interleaved structure is improved and its interesting Local Coordinated Shifting (LCS) Property which is helpful in constructing longer sequences is emphasized. Then, making use of the interleaved structure, several methods for constructing perfect ternary sequences and three-level autocorrelation (0, 1) binary sequences are proposed. The LCS property and the demonstrational construction methods imply that this new interleaved structure is an interesting approach for constructing new sequences.