Regularization in convolutional neural networks (CNNs) is usually addressed with dropout layers. However, dropout is sometimes detrimental in the convolutional part of a CNN as it simply sets to zero a percentage of pixels in the feature maps, adding unrepresentative examples during training. Here, we propose a CNN layer that performs regularization by applying random rotations of reflections to a small percentage of feature maps after every convolutional layer. We prove how this concept is beneficial for images with orientational symmetries, such as in medical images, as it provides a certain degree of rotational invariance. We tested this method in two datasets, a patch-based set of histopathology images (PatchCamelyon) to perform classification using a generic DenseNet, and a set of specular microscopy images of the corneal endothelium to perform segmentation using a tailored U-net, improving the performance in both cases.