Computed tomography angiography (CTA) is an established tool for vessel imaging. Yet, high-intense structures in the contrast image can seriously hamper luminal visualisation. This can be solved by subtraction CTA, where a native image is subtracted from the contrast image. However, patient and organ motion limit the application of this technique. Within this paper, a fully automated intensity-based nonrigid 3D registration algorithm for subtraction CT angiography is presented, using a penalty term to avoid volume change during registration. Visual and automated validation on four clinical datasets clearly show that the algorithm strongly reduces motion artifacts in subtraction CTA. With our method, 39% to 99% of the artifacts disappear, also those caused by minimal displacement of stents or calcified plaques. This results in a better visualisation of the vessel lumen, also of the smaller vessels, allowing a faster and more accurate inspection of the whole vascular structure, especially in case of stenosis.