A double watermarking algorithm for medical image tamper detection is proposed to address the imbalance between robustness and transparency caused by embedding watermark information in medical images. First, the Sine-Cubic chaotic map encryption algorithm is used to linearly couple the Sine map and Cubic map, and the obtained chaotic sequence is used to encrypt the copyright image. Second, the carrier image is wavelet transformed, and the low-frequency sub-band is divided into safety regions. The medical image is divided into regions of interest (ROI) and non-interest (NROI) based on the entropy value of the sub-block in the safety region. Simultaneously, a strong zero watermark is created by combining the stable features of the ROI region and the encrypted copyright. Finally, the zero watermark is embedded into the maximum coefficient of the upper triangular matrix of Schur decomposition of the NROI sub-block of the medical image, and the maximum coefficient following the watermark embedding is recorded for tamper detection. The experimental results demonstrate that the proposed watermarking algorithm is imperceptible, robust, and secure, and can accurately locate the tampered watermarked region; when compared to other watermarking algorithms, the proposed double watermarking algorithm is significantly more robust and efficient.