Convolutional neural networks (CNN) are widely used in computer vision, especially in image classification. However, the way in which information and invariance properties are encoded through in deep CNN architectures is still an open question. In this paper, we propose to modify the standard convo-lutional block of CNN in order to transfer more information layer after layer while keeping some invariance within the network. Our main idea is to exploit both positive and negative high scores obtained in the convolution maps. This behavior is obtained by modifying the traditional activation function step before pooling. We are doubling the maps with specific activations functions, called MaxMin strategy, in order to achieve our pipeline. Extensive experiments on two classical datasets, MNIST and CIFAR-10, show that our deep MaxMin convolutional net outperforms standard CNN.