In recent years Deep Learning has brought about a breakthrough in Medical Image Segmentation. In this regard, U-Net has been the most popular architecture in the medical imaging community. Despite outstanding overall performance in segmenting multimodal medical images, through extensive experimentations on some challenging datasets, we demonstrate that the classical U-Net architecture seems to be lacking in certain aspects. Therefore, we propose some modifications to improve upon the already state-of-the-art U-Net model. Following these modifications, we develop a novel architecture, MultiResUNet, as the potential successor to the U-Net architecture. We have tested and compared MultiResUNet with the classical U-Net on a vast repertoire of multimodal medical images. Although only slight improvements in the cases of ideal images are noticed, remarkable gains in performance have been attained for the challenging ones. We have evaluated our model on five different datasets, each with their own unique challenges, and have obtained a relative improvement in performance of 10.15%, 5.07%, 2.63%, 1.41%, and 0.62% respectively. We have also discussed and highlighted some qualitatively superior aspects of MultiResUNet over classical U-Net that are not really reflected in the quantitative measures.