Principal component analysis is one of the most important methods of multivariate analysis, and has been applied in a wide range of fields such as statistical analysis, machine learning, pattern recognition, signal processing, and communication. Recently, using the idea of multi-agent networks, distributed algorithms for principal component analysis have been proposed for the case where the data matrix is partitioned either row-wise or column-wise. In this paper, considering the case where the data matrix is partitioned both row-wise and column-wise, we propose a new algorithm that allows a multi-agent network to perform principal component analysis in a distributed manner. We also verify its validity by numerical experiments. The proposed algorithm is based on the power method for principal component analysis and the average consensus algorithm.