A method and apparatus produce angiographic magnetic resonance (MR) images that are based on unsaturated spins flowing into an imaging volume, wherein vessels of the person under examination that do not run parallel to a coordinate axis of the MR apparatus are imaged. The nuclear magnetization in at least a first imaging slice of the person under examination is excited in order to generate MR signals in at least one imaging slice, and MR signals from the at least one first imaging slice are received in order to produce angiographic MR images of the vessels. The at least imaging slice has a curved slice profile.