We report a study of demagnetization protocols for frustrated arrays of interacting single domain permalloy nanomagnets by rotating the arrays in a changing magnetic field. The most effective demagnetization is achieved by not only stepping the field strength down while the sample is rotating, but by combining each field step with an alternation in the field direction. By contrast, linearly decreasing the field strength or stepping the field down without alternating the field direction leaves the arrays with a larger remanent magnetic moment. These results suggest that non-monotonic variations in field magnitude around and below the coercive field are important for the demagnetization process.