Although significant efforts have been made in developing nonnegative blind source separation techniques, accurate separation of positive yet dependent sources remains a challenging task. In this paper, a joint correlation function of multiple signals is proposed to reveal and confirm that the observations after nonnegative mixing would have higher joint correlation than the original unknown sources. Accordingly, a new nonnegative least-correlated component analysis (nLCA) method is proposed to design the unmixing matrix by minimizing the joint correlation function among the estimated nonnegative sources. In addition to a closed-form solution for unmixing two mixtures of two sources, the general algorithm of nLCA for the multisource case is developed based on an iterative volume maximization (IVM) principle and linear programming. The source identifiability and required conditions are discussed and proven. The proposed nLCA algorithm, denoted by nLCA-IVM, is evaluated with both simulation data and real biomedical data to demonstrate its superior performance over several existing benchmark methods.