LU Factorization is a triangular decomposition approach of non-singular matrix, and the digital image can be seen as a matrix. Based on the characteristics of the LU Factorization, this paper presents a novel robust watermarking algorithm in wavelet domain of digital image. Firstly, the original image will be transformed into wavelet domain by DWT, and the level of which is decided by the volume of watermark information. Next to do is computing the variances of the last details, and select detail matrix information whose variance is the max one among details. Then it will be preprocessed, if the image matrix is singular matrix, it will be converted into a non-singular matrix by permutation matrix which can be as a key; Secondly, the preprocessed image is decomposed into two triangular matrices including the upper one and the lower one with 1's on the main diagonal, and which have good distribution; Finally, the scrambled meaningful watermark is embedded into the non-zero pixels of two triangular matrixes adaptively. The experimental results show that the algorithm is simple, with better robustness and security.