Binary Neural Networks (BNNs) are neural networks which use binary weights and activations instead of the typical 32-bit floating point values. They have reduced model sizes and allow for efficient inference on mobile or embedded devices with limited power and computational resources. However, the binarization of weights and activations leads to feature maps of lower quality and lower capacity and thus a drop in accuracy compared to traditional networks. Previous work has increased the number of channels or used multiple binary bases to alleviate these problems. In this paper, we instead present an architectural approach: MeliusNet. It consists of alternating a DenseBlock, which increases the feature capacity, and our proposed ImprovementBlock, which increases the feature quality. Experiments on the ImageNet dataset demonstrate the superior performance of our MeliusNet over a variety of popular binary architectures with regards to both computation savings and accuracy. Furthermore, with our method we trained BNN models, which for the first time can match the accuracy of the popular compact network MobileNet-v1 in terms of model size, number of operations and accuracy. Our code is published online at https://github.com/hpi-xnor/BMXNet-v2