The firefly algorithm (FA) is one of the swarm intelligence algorithms for which opposition-based learning (OBL) is an efficient method for improving performance. In most of the existing OBL schemes, the opposite solution is calculated simultaneously for all dimensions of the original solution. However, the opposite solution does not always offer a better value in every dimension than the original solution. This paper develops a new scheme by utilizing the orthogonal experiment design method to select a subset of elements of the individual to be changed into opposite values by the centroid opposition, while the rest remain unchanged. Useful information about the original individual and its opposite can be found by this method. This new scheme is named orthogonal centroid opposition-based learning (OCOBL) and is incorporated into FA to obtain an orthogonal centroid opposition-based firefly algorithm (OCOFA). OCOFA is tested on the CEC's 2013 benchmark suite and compared with state-of-the-art FA variants. The experimental results demonstrate the effectiveness of OCOBL and an improved performance for the proposed OCOFA.