Non-contrast-enhanced time of flight (TOF) is a standard method for magnetic resonance angiography used to depict vessel morphology. TOF is commonly performed with a 3D steady-state acquisition, employing a short repetition time to support high resolution imaging. At 7 T, TOF exhibits substantial increase in SNR and contrast, improving its clinical value. However, one of the remaining challenges, exacerbated at 7 T, is the presence of artifacts due to pulsatile blood flow, especially near major blood vessels. In this study we examine a method to significantly reduce these artifacts. We recently introduced a new "local-scrambling" approach that semi-randomizes the acquisition order of the phase encodes, to achieve a controllable cutoff frequency above which the artifacts are drastically reduced. With this approach, artifacts resulting from fast local fluctuations such as cardiac pulsation are significantly reduced. In this study, we explore the ability of this local-scrambling approach to reduce pulsatile blood flow artifacts in a 3D TOF acquisition. Cartesian line-by-line and center-out ordering, with and without local-scrambling, were compared in simulations and in human brain imaging at 3 and 7 T scanners. In the simulations the artifact intensity showed a 10-fold reduction using local-scrambling compared to line-by-line and 4-fold compared to center-out ordering. In vivo results show that artifacts are much more pronounced at 7 T compared to 3 T, and in both cases they are effectively reduced by local-scrambling. Local-scrambling improves image quality for both line-by-line and center-out ordering. This approach can easily be implemented in the scanner without any changes to the reconstruction.