We introduce Classification with Alternating Normalization (CAN), a non-parametric post-processing step for classification. CAN improves classification accuracy for challenging examples by re-adjusting their predicted class probability distribution using the predicted class distributions of high-confidence validation examples. CAN is easily applicable to any probabilistic classifier, with minimal computation overhead. We analyze the properties of CAN using simulated experiments, and empirically demonstrate its effectiveness across a diverse set of classification tasks.