The problem of band selection (BS) is of great importance to handle the curse of dimensionality for hyperspectral image (HSI) applications (e.g., classification). This letter proposes an unsupervised BS approach based on a split-and-merge concept. This new approach provides relevant spectral sub-bands by splitting the adjacent bands without violating the physical meaning of the spectral data. Next, it merges highly correlated bands and sub-bands to reduce the dimensionality of the HSI. Experiments on three public data sets and comparison with state-of-the-art approaches show the efficiency of the proposed approach.