The resurgence of deep neural networks has created an alternative pathway for low-dose computed tomography denoising by learning a nonlinear transformation function between low-dose CT (LDCT) and normal-dose CT (NDCT) image pairs. However, those paired LDCT and NDCT images are rarely available in the clinical environment, making deep neural network deployment infeasible. This study proposes a novel method for self-supervised low-dose CT denoising to alleviate the requirement of paired LDCT and NDCT images. Specifically, we have trained an invertible neural network to minimize the pixel-based mean square distance between a noisy slice and the average of its two immediate adjacent noisy slices. We have shown the aforementioned is similar to training a neural network to minimize the distance between clean NDCT and noisy LDCT image pairs. Again, during the reverse mapping of the invertible network, the output image is mapped to the original input image, similar to cycle consistency loss. Finally, the trained invertible network's forward mapping is used for denoising LDCT images. Extensive experiments on two publicly available datasets showed that our method performs favourably against other existing unsupervised methods.