Numerous modern optimization and machine learning algorithms rely on\nsubgradient information being trustworthy and hence, they may fail to converge\nwhen such information is corrupted. In this paper, we consider the setting\nwhere subgradient information may be arbitrarily corrupted (with a given\nprobability) and study the robustness properties of the normalized subgradient\nmethod. Under the probabilistic corruption scenario, we prove that the\nnormalized subgradient method, whose updates rely solely on directional\ninformation of the subgradient, converges to a minimizer for convex, strongly\nconvex, and weakly-pseudo convex functions satisfying certain conditions.\nNumerical evidence on linear regression and logistic classification problems\nsupport our results.\n