Medical images are useful for the treatment process. They contain a lot of information on displaying abnormalities in your body. The contour of medical images is a matter of interest. In there, edge detection is a process prepared for boundaries. Therefore, the edge detection of medical images is very important. Other previous methods must sacrifice time for the accurate results. It is because the medical images in the real world have many impurities. In this paper, I propose a method of detecting edges in medical images which have impurities by using augmented lagrangian method to improve the Canny algorithm. My algorithm improves the ability to detect edges faster. Compared with other recent methods, the proposed method is more efficient.