This paper proposes a blind digital audio watermarking algorithm that utilizes the quantization index modulation (QIM) and the singular value decomposition (SVD) of stereo audio signals. Conventional SVD-based blind audio watermarking algorithms lack physical interpretation since the matrix construction method for the input matrix for SVD is heuristically defined. However, in the proposed approach, because the SVD is directly applied to the stereo input signals, the resulting decomposed elements convey a conceptually meaningful interpretation of the original audio signal. As the proposed approach effectively utilizes the ratio of singular values, the embedded watermark is highly imperceptible and robust against volumetric scaling attacks; most QIM-based watermarking schemes are weak to these types of attacks. Experimental results under well-known practical attacks, such as compressions, resampling, and various types of signal processing, confirm that the proposed algorithm performs well compared to conventional audio watermarking algorithms.