Long scan times limit the application of 4D flow in clinical practice. Even at 7T, considerable scan times are needed for modest spatiotemporal resolutions. This work demonstrates the advantage of Compressed Sensing acceleration of 4D flow MRI at 7T with a novel undersampling technique. Healthy subjects (n=5) were scanned using standard SENSE and a proposed undersampling technique with Compressed Sensing reconstruction. Flow analysis showed minor differences, and image quality improved for Compressed Sensing reconstructions with maintained resolution and reduced scan time. The method enables further increases of acceleration and spatiotemporal resolution, adding more physiological details beyond current resolution limitations.