In this work we propose a Repetitive Index Modulation (RIM) based digital watermarking scheme for authentication and integrity verification of medical images. Exploiting the fact that many types of medical images have significant background areas and medically meaningful Regions Of Interest (ROI), which represent the actual contents of the images, the scheme uses the contents of the ROI to create a content-dependent watermark and embeds the watermark in the background areas. Therefore when any pixel of the ROI is attacked, the watermark embedded in the background areas will be different from the watermark calculated according to the attacked contents, thus raising alarm that the image in question is inauthentic. Because the creation of the watermark is content-dependent and the watermark is only embedded in the background areas, the proposed scheme can actually protect the content/ROI without distorting it.