Denoising of magnetic resonance images is beneficial in improving the quality of low signal-to-noise ratio images. Recently, denoising using deep neural networks has demonstrated promising results. Most of these networks, however, utilize supervised learning, which requires large training images of noise-corrupted and clean image pairs. Obtaining training images, particularly clean images, is expensive and time-consuming. Hence, methods such as Noise2Noise (N2N) that require only pairs of noise-corrupted images have been developed to reduce the burden of obtaining training datasets. In this study, we propose a new self-supervised denoising method, Coil2Coil (C2C), that does not require the acquisition of clean images or paired noise-corrupted images for training. Instead, the method utilizes multichannel data from phased-array coils to generate training images. First, it divides and combines multichannel coil images into two images, one for input and the other for label. Then, they are processed to impose noise independence and sensitivity normalization such that they can be used for the training images of N2N. For inference, the method inputs a coil-combined image (e.g., DICOM image), enabling a wide application of the method. When evaluated using synthetic noise-added images, C2C shows the best performance against several self-supervised methods, reporting comparable outcomes to supervised methods. When testing the DICOM images, C2C successfully denoised real noise without showing structure-dependent residuals in the error maps. Because of the significant advantage of not requiring additional scans for clean or paired images, the method can be easily utilized for various clinical applications.