Biomedical image segmentation plays an important role in quantitative analysis, clinical diagnosis, and medical manipulation. Objects in medical images have different scales, types, complex backgrounds, and similar tissue appearances, making information extraction challenging. To solve this problem, a module is proposed that takes into account the features of images, which will improve the biomedical image segmentation network FE-Net. An integral part of the FE-Net algorithm is the connection skipping mechanism, which ensures the connection and fusion of feature maps from different layers in the encoder and decoder. Features at the encoder level are combined with high-level semantic knowledge at the decoder level. The algorithm establishes connections between feature maps, which is used in medicine for image processing. The proposed method is tested on three public datasets: Kvasir-SEG, CVC-ClinicDB and 2018 Data Science Bowl. Based on the results of the study, it was found that FE-Net demonstrates better performance compared to other methods in terms of Intersection over Union and F1-score. The network under consideration copes more effectively with segmentation details and object boundaries, while maintaining high accuracy. The study was conducted jointly with the Department of Magnetic Resonance Imaging of the N. N. Alexandrov National Oncology Center. Access to the source code of the algorithm and additional technical details is available at https://github.com/tyjcbzd/FE-Net.