In this paper, a reversible integer-to-integer wavelet transform based on non-separable 2D allpass filters is proposed for lossless image coding. The number of rounding operations included in the reversible wavelet transform is reduced by using non-separable 2D allpass filters, thus it is expected to get better coding performance. The lossless coding performance of the proposed reversible wavelet transform is evaluated and compared with the conventional separable wavelet transforms. It is shown from the experimental results that the proposed non-separable 2D reversible wavelet transform can achieve better lossless coding performance than the conventional separable wavelet transforms, including the D-5/3 wavelet transform in the JPEG 2000.