We consider a class-incremental semantic segmentation (CISS) problem. While some recently proposed algorithms utilized variants of knowledge distillation (KD) technique to tackle the problem, they only partially addressed the key additional challenges in CISS that causes the catastrophic forgetting; \textit{i.e.}, the semantic drift of the background class and multi-label prediction issue. To better address these challenges, we propose a new method, dubbed as SSUL-M (Semantic Segmentation with Unknown Label with Memory), by carefully combining several techniques tailored for semantic segmentation. More specifically, we make three main contributions; (1) modeling \textit{unknown} class within the background class to help learning future classes (help plasticity), (2) \textit{freezing} backbone network and past classifiers with binary cross-entropy loss and pseudo-labeling to overcome catastrophic forgetting (help stability), and (3) utilizing \textit{tiny exemplar memory} for the first time in CISS to improve \textit{both} plasticity and stability. As a result, we show our method achieves significantly better performance than the recent state-of-the-art baselines on the standard benchmark datasets. Furthermore, we justify our contributions with thorough and extensive ablation analyses and discuss different natures of the CISS problem compared to the standard class-incremental learning for classification. The official code is available at https://github.com/clovaai/SSUL.