In the framework of convolutional neural networks that lie at the heart of deep learning, downsampling is often performed with a max-pooling operation that only retains the element with maximum activation, while completely discarding the information contained in other elements in a pooling region. To address this issue, a novel pooling scheme, Ordinal Pooling Network (OPN), is introduced in this work. OPN rearranges all the elements of a pooling region in a sequence and assigns different weights to these elements based upon their orders in the sequence, where the weights are learned via the gradient-based optimisation. The results of our small-scale experiments on image classification task demonstrate that this scheme leads to a consistent improvement in the accuracy over max-pooling operation. This improvement is expected to increase in deeper networks, where several layers of pooling become necessary.