A method and a computed tomography unit are disclosed, that render it possible in a simple way to remove ring artifacts from tomograms I.sub.k, particularly in the case of a fast feed of the recording region per revolution of the recording system of the computed tomography unit by calculating a ring artifact image I.sub.k for each tomogram I.sub.k. In this procedure, temporary ring artifact images Rt.sub.k are firstly calculated for each tomogram I.sub.k, and subsequently the final ring artifact image R.sub.k is formed for the purpose of correcting the respective tomogram I.sub.k by averaging over at least a portion T.sub.sub of the temporary ring artifact images Rt.sub.k, the temporary ring artifact images Rt.sub.k being rotated before averaging in such a way that the ring artifacts present in the temporary artifact images Rt.sub.k substantially coincide and their position substantially corresponds to the ring artifacts present in the tomogram I.sub.k.