Digital technology and the widespread use of the Internet has increased the speeds at which digital data can be obtained and shared in daily life. In parallel to this, there are important concerns regarding the confidentiality of private data during data transmissions and the possibility that data might fall into the hands of third parties. Issues relating to data safety can also affect patients' medical images and other information relating to these images. In this study, we propose a new method based on block matching that can be used to hide the patient information in medical images. In this method, 8 scanning orders (6 of which are newly designed) are developed to provide high image quality. By diversifying the number of scanning orders, we aim to achieve the lowest number of bit changes. The performance of the developed method is measured using the number of bits subject to change, the peak signal-to-noise ratio and the mean structural similarity index measure image quality assessment metrics, and steganalysis attacks. The method we developed was found to be more effective in hiding data compared to the classical least significant bit method.