Deep neural network (DNN)-based speech enhancement usually uses a clean speech as a training target. However, it is hard to collect large amounts of clean speech because the recording is very costly. In other words, the performance of current speech enhancement has been limited by the amount of training data. To relax this limitation, Noisy-target Training (NyTT) that utilizes noisy speech as a training target has been proposed. Although it has been experimentally shown that NyTT can train a DNN without clean speech, a detailed analysis has not been conducted and its behavior has not been understood well. In this paper, we conduct various analyses to deepen our understanding of NyTT. In addition, based on the property of NyTT, we propose a refined method that is comparable to the method using clean speech. Furthermore, we show that we can improve the performance by using a huge amount of noisy speech with clean speech.