We present a new 16-QAM near complementary sequence construction where the length of the sequences is n = 2m. The 16-QAM near complementary sequences are constructed by nonlinear offsets. But the peak-to-mean envelope power ratio bounds for these 16-QAM near complementary sequences is as low as 2.4. The number of newly constructed 16-QAM near complementary sequences is ([(m!)/2])4m+1.