Librarians at the National Library of Medicine tag each biomedical abstract to be indexed by their Pubmed information system with terms from the Medical Subject Headings (MeSH) terminology. The MeSH terminology has over 26,000 terms and indexers look at each article's full text to assign a set of most suitable terms for indexing it. Several recent automated attempts focused on using the article title and abstract text to identify MeSH terms for the corresponding article. Most of these approaches used supervised machine learning techniques that use already indexed articles and the corresponding MeSH terms. In this paper, we present a novel unsupervised approach using named entity recognition, relationship extraction, and output label co-occurrence frequencies of MeSH term pairs from the existing set of 22 million articles already indexed with MeSH terms by librarians at NLM. The main goal of our study is to gauge the potential of output label co-occurrence statistics and relationships extracted from free text in unsupervised indexing approaches. Especially, in biomedical domains, output label co-occurrences are generally easier to obtain than training data involving document and label set pairs owing to the sensitive nature of textual documents containing protected health information. Our methods achieve a micro F-score that is comparable to those obtained using supervised machine learning techniques with training data consisting of document label set pairs. Baseline comparisons reveal strong prospects for further research in exploiting label co-occurrences and relationships extracted from free text in recommending terms for indexing biomedical articles.