A method and computed tomography unit are disclosed for producing computed tomograms of a patient's beating heart by voxelwise reconstruction of volume data records from prescribed cardiac cycle phases. Firstly, a multiplicity of voxelwise partial reconstructions are calculated from projection segments substantially smaller than 180.degree. in accordance with small cardiac phase segments. The complete voxel data that cover overall at least 180.degree. and originate from a preselected cardiac phase are subsequently summed up per cardiac phase to be considered from the pool of the incomplete reconstructed voxel data.