A method and a computed tomography scanner are disclosed for carrying out an angiographic examination of a patient, wherein the utilized computed tomography scanner includes at least one recording system mounted on a gantry such that it can rotate about a z-axis. Projection data is acquired from at least one prescribed angular position of the gantry for at least two different energies of X-ray radiation. The projection data is subsequently combined to form a resulting projection image by evaluating the projection data corresponding to the respective angular position, in which projection image at least one substance, which should be displayed selectively, is imaged with a high image contrast compared to the respective individual projection data. This procedure extends the field of application of the computed tomography scanner to projection-based angiography examinations, which were previously restricted to C-arm systems. 3D image reconstruction methods and projection methods can be carried out on opposite sides and with great flexibility during an examination, without the need for an additional modality. By using a multispectral technique, it is possible to contrast agent. The projection data at dispense with recording a native projection data record without the different energies are moreover acquired with no or little time offset, and so a computationally expensive and error-prone registration of the data records can be dispensed with.