Hyperspectral remote sensing is capable of providing large numbers of spectral bands. The vast amount of data volume presents challenging problems for information processing, such as heavy computational burden. In this paper, the impact of dimension reduction on hyperspectral data clustering is investigated from two viewpoints: 1) computational complexity; and 2) clustering performance. Clustering is one of the most useful tasks in data mining process. So, investigating the impact of dimension reduction on hyperspectral data clustering is justifiable. The proposed approach is based on thresholding the band correlation matrix and selecting the least correlated bands. Selected bands are then used to cluster the hyperspectral image. Experimental results on a real-world hyperspectral remote sensing data proved that the proposed approach will decrease computational complexity and lead to better clustering results. For evaluating the clustering performance, the Calinski-Harabasz, Davies-Bouldin and Krzanowski-Lai indices are used. These indices evaluate the clustering results using quantities and features inherent in the dataset. In other words, they do not need any external information.