Technological developments for several years have resulted in the handling (storing, exchanging or processing) of increasingly important data in various fields and particularly in medical field. In this works we present a new image compression / decompression algorithm based on the quaternion wavelet transform (QWT). This algorithm is simple, fast and efficient. It has been applied to medical images. The results obtained after decompression are appreciated through the compression parameter values of CR, PSNR, and MSE and by visual observation. By the values of these parameters, the results of the algorithm are considered encouraging.