Multi-instance partial-label learning (MIPL) addresses scenarios where each training sample is represented as a multi-instance bag associated with a candidate label set containing one true label and several false positives. Existing MIPL algorithms have primarily focused on mapping multi-instance bags to candidate label sets for disambiguation, disregarding the intrinsic properties of the label space and the supervised information provided by non-candidate label sets. In this paper, we propose an algorithm named ELIMIPL, i.e., Exploiting conjugate Label Information for Multi-Instance Partial-Label learning, which exploits the conjugate label information to improve the disambiguation performance. To achieve this, we extract the label information embedded in both candidate and non-candidate label sets, incorporating the intrinsic properties of the label space. Experimental results obtained from benchmark and real-world datasets demonstrate the superiority of the proposed ELIMIPL over existing MIPL algorithms and other well-established partial-label learning algorithms.