We consider a novel variant of the contextual bandit problem (i.e., the multi-armed bandit with side-information, or context, available to a decision-maker) where the context used at each decision may be corrupted ("useless context"). This new problem is motivated by certain on-line settings including clinical trial and ad recommendation applications. In order to address the corrupted-context setting, we propose to combine the standard contextual bandit approach with a classical multi-armed bandit mechanism. Unlike standard contextual bandit methods, we are able to learn from all iteration, even those with corrupted context, by improving the computing of the expectation for each arm. Promising empirical results are obtained on several real-life datasets.