To counter the challenge associated with noise labels, the learning strategy of deep neural networks must be differentiated over the learning period during the training process. Therefore, we propose a novel two-phase learning method, MORPH, which automatically transitions its learning phase at the point when the network begins to rapidly memorize false-labeled samples. In the first phase, MORPH starts to update the network for all the training samples before the transition point. Without any supervision, the learning phase is converted to the next phase on the basis of the estimated best transition point. Subsequently, MORPH resumes the training of the network only for a maximal safe set, which maintains the collection of almost certainly true-labeled samples at each epoch. Owing to its two-phase learning, MORPH realizes noise-free training for any type of label noise for practical use. Moreover, extensive experiments using six datasets verify that MORPH significantly outperforms five state-of-the art methods in terms of test error and training time.