A family of near-complementary sequences with peak-to-mean envelope power ratio (PMEPR) < 4 was proposed for peak power control in multicarrier communications by Yu and Gong recently. In this Letter, the PMEPR bound of these near-complementary sequences are improved to asymptotically equivalent to 2. Based on the proof, new near-complementary sequences constructed by other seed pairs are proposed. The PMEPR of these near-complementary sequences are still asymptotically equivalent to 2.