Multi-label learning is a practical machine learning paradigm dealing with instances associated with multiple labels simultaneously. Most existing multi-label learning studies are designed under the closed-world assumption, i.e. a fixed size of label space. However, it encounters significant difficulties in open-set scenarios, where test data may contain unknown labels absent from the training set to be recognized. Existing method typically tackles this challenging problem through sub-labeling approximations and prototype-based comparisons, which often overlooks the implicit information carried by unknown labels. To address this, we propose a novel framework CREM, i.e. Classifier-induced REciprocal point for Multi-label open-set recognition, which rethinks the above problem from the reciprocal point perspective. Specifically, reciprocal points are formulated by explicitly constraining the opposition feature space to a learnable bounded margin. Then reciprocal points can be induced through the classifier with the instance-wise bias eliminated. Subsequently, a unified optimization framework is introduced to jointly facilitate the classifier and reciprocal points induction. Extensive experiments demonstrate the effectiveness and superiority of the proposed CREM approach in the multi-label open-set recognition paradigm.