Semi-supervised learning (SSL) is a classical machine learning paradigm dealing with labeled and unlabeled data. However, it often suffers performance degradation in real-world open-set scenarios, where unlabeled data contains outliers from novel categories that do not appear in labeled data. Existing studies tackle this challenging open-set SSL problem with detect-and-filter strategy, which attempts to purify unlabeled data by detecting and filtering outliers. In this paper, we propose a novel binary decomposition strategy, which refrains from error-prone procedure of outlier detection by directly transforming the original open-set SSL problem into a number of standard binary SSL problems. Accordingly, a concise yet effective approach named BDMatch is presented. BDMatch confronts two attendant issues brought by binary decomposition, i.e. class-imbalance and representation-compromise, with adaptive logit adjustment and label-specific feature learning respectively. Comprehensive experiments on diversified benchmarks clearly validate the superiority of BDMatch as well as the effectiveness of our binary decomposition strategy.