As an effective method for copyright protection of digital products against illegal usage, watermarking in wavelet domain has recently received considerable attention due to the desirable multiresolution property of wavelet transform. In general, images can be represented with different resolutions by the wavelet decomposition, analogous to the human visual system (HVS). Usually, human eyes are insensitive to image singularities revealed by different high frequency subbands of wavelet decomposed images. Hence, adding watermarks into these singularities will improve the imperceptibility that is a desired property of a watermarking scheme. That is, the capability for revealing singularities of images plays a key role in designing wavelet-based watermarking algorithms. Unfortunately, the existing wavelets have a limited ability in revealing singularities in different directions. This motivates us to construct new wavelet filter banks that can reveal singularities in all directions. In this paper, we utilize special symmetric matrices to construct the new nontensor product wavelet filter banks, which can capture the singularities in all directions. Empirical studies will show their advantages of revealing singularities in comparison with the existing wavelets. Based upon these new wavelet filter banks, we, therefore, propose a modified significant difference watermarking algorithm. Experimental results show its promising results.