In recent years, deep neural networks have achieved remarkable accuracy in computer vision tasks. With inference time being a crucial factor, particularly in dense prediction tasks such as semantic segmentation, knowledge distillation has emerged as a successful technique for improving the accuracy of lightweight student networks. The existing methods often neglect the information in channels and among different classes.To overcome these limitations, this paper proposes a novel method called Inter-Class Similarity Distillation (ICSD) for the purpose of knowledge distillation. The proposed method transfers high-order relations from the teacher network to the student network by independently computing intra-class distributions for each class from network outputs. This is followed by calculating inter-class similarity matrices for distillation using KL divergence between distributions of each pair of classes. To further improve the effectiveness of the proposed method, an Adaptive Loss Weighting (ALW) training strategy is proposed. Unlike existing methods, the ALW strategy gradually reduces the influence of the teacher network towards the end of training process to account for errors in teacher's predictions. Extensive experiments conducted on two well-known datasets for semantic segmentation, Cityscapes and Pascal VOC 2012, validate the effectiveness of the proposed method in terms of mIoU and pixel accuracy. The proposed method outperforms most of existing knowledge distillation methods as demonstrated by both quantitative and qualitative evaluations. Code is available at: https://github.com/AmirMansurian/AICSD