Transform coding has been used successfully for radiological image compression in the picture archival and communication system (PACS) and other applications. However, it suffers from the artifact known as 'blocking effect' due to division of subblocks, which is very undesirable in the clinical environment. In this paper, we propose a combined-transform coding (CTC) scheme to reduce this effect and achieve better subjective performance. In the combined- transform coding scheme, we first divide the image into two sets that have different correlation properties, namely the upper image set (UIS) and lower image set (LIS). The UIS contains the most significant information and more correlation, and the LIS contains the less significant information. The UIS is compressed noiselessly without dividing into blocks and the LIS is coded by conventional block transform coding. Since the correlation in UIS is largely reduced (without distortion), the inter-block correlation, and hence the 'blocking effect,' is significantly reduced. This paper first describes the proposed CTC scheme and investigates its information-theoretic properties. Then, computer simulation results for a class of AP view chest x-ray images are presented. The comparison between the CTC scheme and conventional Discrete Cosine Transform (DCT) and Discrete Walsh-Hadmad Transform (DWHT) is made to demonstrate the performance improvement of the proposed scheme. The advantages of the proposed CTC scheme also include (1) no ringing effect due to no error propagation across the boundary, (2) no additional computation and (3) the ability to hold distortion below a certain threshold. In addition, we found that the idea of combined-coding can also be used in noiseless coding, and slight improvement in the compression performance can also be achieved if used properly. Finally, we point out that this scheme has its advantages in medical image transmission over a noisy channel or the packet-switched network in case of channel error and packet loss.