In many image denoising tasks, the difficulty of collecting noisy/clean image pairs limits the application of supervised CNNs. We consider such a case in which paired data and noise statistics are not accessible, but unpaired noisy and clean images are easy to collect. To form the necessary supervision, our strategy is to extract the noise from the noisy image to synthesize new data. To ease the interference of the image background, we use a noise removal module to aid noise extraction. The noise removal module first roughly removes noise from the noisy image, which is equivalent to excluding much background information. A noise approximation module can therefore easily extract a new noise map from the removed noise to match the gradient of the noisy input. This noise map is added to a random clean image to synthesize a new data pair, which is then fed back to the noise removal module to correct the noise removal process. These two modules cooperate to extract noise finely. After convergence, the noise removal module can remove noise without damaging other background details, so we use it as our final denoising network. Experiments show that the denoising performance of the proposed method is competitive with other supervised CNNs.