Approximate k NN ( k -nearest neighbor) techniques using binary hash functions are among the most commonly used approaches for overcoming the prohibitive cost of performing exact k NN queries. However, the success of these techniques largely depends on their hash functions' ability to distinguish k NN items; that is, the k NN items retrieved based on data items' hashcodes , should include as many true k NN items as possible. A widely-adopted principle for this process is to ensure that similar items are assigned to the same hashcode so that the items with the hashcodes similar to a query's hashcode are likely to be true neighbors. In this work, we abandon this heavily-utilized principle and pursue the opposite direction for generating more effective hash functions for k NN tasks. That is, we aim to increase the distance between similar items in the hashcode space, instead of reducing it. Our contribution begins by providing theoretical analysis on why this revolutionary and seemingly counter-intuitive approach leads to a more accurate identification of k NN items. Our analysis is followed by a proposal for a hashing algorithm that embeds this novel principle. Our empirical studies confirm that a hashing algorithm based on this counter-intuitive idea significantly improves the efficiency and accuracy of state-of-the-art techniques.