In biomedical natural language processing, named entity recognition (NER) and named entity normalization (NEN) are key tasks that enable the automatic extraction of biomedical entities (e.g. diseases and drugs) from the ever-growing biomedical literature. In this article, we present BERN2 (Advanced Biomedical Entity Recognition and Normalization), a tool that improves the previous neural network-based NER tool by employing a multi-task NER model and neural network-based NEN models to achieve much faster and more accurate inference. We hope that our tool can help annotate large-scale biomedical texts for various tasks such as biomedical knowledge graph construction.