Abstract: Class-incremental semantic segmentation (CISS) labels each pixel of an image with a corresponding object/stuff class continually. To this end, it is crucial to learn novel classes incrementally without forgetting previously learned knowledge. Current CISS methods typically use a knowledge distillation (KD) technique for preserving classifier logits, or freeze a feature extractor, to avoid the forgetting problem. The strong constraints, however, prevent learning discriminative features for novel classes. We introduce a CISS framework that alleviates the forgetting problem and facilitates learning novel classes effectively. We have found that a logit can be decomposed into two terms. They quantify how likely an input belongs to a particular class or not, providing a clue for a reasoning process of a model. The KD technique, in this context, preserves the sum of two terms ($\textit{i.e.}$, a class logit), suggesting that each could be changed and thus the KD does not imitate the reasoning process. To impose constraints on each term explicitly, we propose a new decomposed knowledge distillation (DKD) technique, improving the rigidity of a model and addressing the forgetting problem more effectively. We also introduce a novel initialization method to train new classifiers for novel classes. In CISS, the number of negative training samples for novel classes is not sufficient to discriminate old classes. To mitigate this, we propose to transfer knowledge of negatives to the classifiers successively using an auxiliary classifier, boosting the performance significantly. Experimental results on standard CISS benchmarks demonstrate the effectiveness of our framework.