Web data such as documents, images, and videos are examples of large matrices. To deal with such matrices, one may use matrix decomposition techniques. As such, CUR matrix decomposition is an important approximation technique for high-dimensional data. It approximates a data matrix by selecting a few of its rows and columns. However, a problem faced by most CUR decomposition matrix methods is that they ignore the correlation among columns (rows), which gives them lesser chance to be selected; even though, they might be appropriate candidates for basis vectors. In this paper, a novel CUR matrix decomposition method is proposed, in which calculation of the correlation, boosts the chance of selecting such columns (rows). Experimental results indicate that in comparison with other methods, this one has had higher accuracy in matrix approximation.