Human beings may make random guesses in decision-making. Occasionally, their guesses may generate consistency with the real situation. This kind of consistency is termed random consistency. In the area of machine leaning, the randomness is unavoidable and ubiquitous in learning algorithms. However, the accuracy (A), which is a fundamental performance measure for machine learning, does not recognize the random consistency. This causes that the classifiers learnt by A contain the random consistency. The random consistency may cause an unreliable evaluation and harm the generalization performance. To solve this problem, the pure accuracy (PA) is defined to eliminate the random consistency from the A. In this paper, we mainly study the necessity, learning consistency and leaning method of the PA. We show that the PA is insensitive to the class distribution of classifier and is more fair to the majority and the minority than A. Subsequently, some novel generalization bounds on the PA and A are given. Furthermore, we show that the PA is Bayes-risk consistent in finite and infinite hypothesis space. We design a plug-in rule that maximizes the PA, and the experiments on twenty benchmark data sets demonstrate that the proposed method performs statistically better than the logistic regression in terms of PA and comparable performance in terms of A. Compared with the other plug-in rules that optimize the PA, the proposed method obtains much better performance.