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Canonical correlation analysis (CCA) is one of the most well-known methods to extract features from multi-view data and has attracted much attention in recent years. However, classical CCA is unsupervised and does not take class label information into account. In this paper, we introduce the within-class cross correlation into CCA and propose a new method called canonical Random Correlation Analysis (RCA). In RCA, besides considering the correlation between two views from the same sample, the cross correlations between two views respectively from different within-class samples are also used to achieve good performance. Two approaches for randomly generating cross correlation samples are developed.