A well-known color constancy method is based on the GreyWorld assumption i.e. the average reflectance of surfaces in the world is achromatic. In this article we propose a new hypothesis for color constancy, namely the Grey-Edge hypothesis assuming that the average edge difference in a scene is achromatic. Based on this hypothesis, we propose an algorithm for color constancy. Recently, the Grey-World hypothesis and the max-RGB method were shown to be two instantiations of a Minkowski norm based color constancy method. Similarly we also propose a more generale version of the Grey-Edge hypothesis which assumes that the Minkowsky norm of derivatives of the reflectance of surfaces is achromatic. The algorithms are tested on a large data set of images under different illuminants, and the results show that the new method outperforms the Grey-World assumption and the max-RGB method. Results are comparable to more elaborate algorithms, however at lower computational costs.