On the basis of the Karush-Kuhn-Tucker (KKT) theorem, a novel digital audio watermarking scheme is proposed. To guarantee the robustness of a watermark, this scheme embeds information into low-frequency coefficients of audio's discrete wavelet transform. For the modification of low-frequency amplitude, this study uses the KKT theorem to minimise the difference between the original and the watermarked coefficients. Accordingly, embedding strength is increased to enhance the most robustness of a watermarked audio under sufficient embedding capacity and audio quality. In addition, the proposed watermarking scheme can extract the hidden data without the knowledge of original audio signal. Experimental results indicate that the performance of the proposed scheme is mostly better than other amplitude modification methods.