Due to the bandwidth and storage limitations, medical images must be compressed before transmission and storage. However, the compression will reduce the image fidelity, especially when the images are compressed at lower bit rates. The reconstructed images suffer from blocking artifacts and the image quality will be severely degraded under the circumstance of high compression ratios. In this paper, we present a strategy to increase the compression ratio with simple computational burden and excellent decoded quality. We regard the discrete cosine transform as a bandpass filter to decompose a sub-block into equal-sized bands. After a band gathering operation, a high similarity property among bands is found. By the utilization of similarity property, the bit rate of compression can be greatly reduced. Meanwhile, the characteristics of the original image are not sacrificed. Thus, it can avoid the misdiagnosis of diseases for doctors. Simulations are carried to different kind of medical images to demonstrate that the proposed method achieves better performance when compared to other existing transform coding scheme as the JPEG in terms of bit rate and quality. For the case of angiogram image, its peak signal-to-noise-ratio gain is 13.5 dB at the same bit rate of 0.15 bits per pixel when comparing to the JPEG compression. As to the other kind of medical images, their benefits are not so obvious as an angiogram image; however, the gains for them are still from 4-8 dB at high compression ratios. Two doctors from the Department of Radiology, National Cheng Kung University Hospital, Tainan, Taiwan, R.O.C., and Chang Gung Medical Hospital, Kaoshuing, Taiwan, R.O.C., are invited to verify the decoded image quality; the diagnoses of all the test images are correct when the compression ratios are below 20.