Combining redundant discrete wavelet transform (RDWT) with matrix Schur composition, we propose a new digital watermarking algorithm for gray image blind detection. The algorithm firstly performs secondary RDWT on the carrier image and extracts the low frequency part of the approximate subgraph. Then Schur decomposition is performed on the low frequency coefficients of each block after blocking procession, and the maximum energy elements on the diagonal of the upper triangular matrix are modified to complete the embedding of the watermark image which is encrypted by the Fibonacci transformation. Therefore, the watermark extraction process can achieve blind extraction. Experimental results show that the watermark embedding time of the proposed watermarking algorithm is only 0.97s, and the average watermark extraction time is 0.211s. Compared with similar blind watermarking algorithms, the PSNR value of invisibility is increased by 14.12%, and the resistance to Gaussian noise, salt and pepper noise attack and shear geometric attack by 21.32%, 17.31% and 27.83% respectively.