Image coding based on the wavelet transform with a lifting configuration has received considerable attention in recent years as a method for unified lossless and nonlossless coding, because effective lossless coding becomes possible by rounding after filter processing. However, if rounding is also performed for lossy coding, rounding errors in addition to quantization errors are superposed on the reconstructed image, so that a further reduction of the SNR takes place. In this paper, a conversion module of a new nonseparable two-dimensional wavelet that can be extended to a general N-stage problem is proposed. In this way, unified lossless and lossy coding with reduced rounding error is possible in addition to interchangeability with the conventional separable wavelet. Further, the propagation mechanism of the rounding error within the filter bank is analyzed. The variance of the rounding errors superposed on the reconstructed image is theoretically derived. In this way, the reduction effect of the rounding error in the N stages is theoretically explained. As a result, the variance of the rounding error is reduced by about 50% in comparison with that for the separable case and an SNR improvement of about 1.30 dB on the average at the time of high-bit-rate lossy coding is confirmed. © 2005 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 88(5): 37–49, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.20124