Medical image registration plays a vital role in medical image processing. Extracting expressive representations for medical images is crucial for improving the registration quality. One common practice for this end is constructing a convolutional backbone to enable interactions with skip connections among feature extraction layers. The de facto structure, U-Net-like networks, has attempted to design skip connections such as nested or full-scale ones to connect one single encoder and one single decoder to improve its representation capacity. Despite being effective, it still does not fully explore interactions with a single encoder and decoder architectures. In this paper, we embrace this observation and introduce a simple yet effective alternative strategy to enhance the representations for registrations by appending one additional decoder. The new decoder is designed to interact with both the original encoder and decoder. In this way, it not only reuses feature presentation from corresponding layers in the encoder but also interacts with the original decoder to corporately give more accurate registration results. The new architecture is concise yet generalized, with only one encoder and two decoders forming a ``Tetrahedron'' structure, thereby dubbed Tetrahedron-Net. Three instantiations of Tetrahedron-Net are further constructed regarding the different structures of the appended decoder. Our extensive experiments prove that superior performance can be obtained on several representative benchmarks of medical image registration. Finally, such a ``Tetrahedron'' design can also be easily integrated into popular U-Net-like architectures including VoxelMorph, ViT-V-Net, and TransMorph, leading to consistent performance gains.