We proposed an efficient unsupervised band selection method, maximum ellipsoid volume triangular factorization (MEV–TF), which is based on MEV and TF. MEV band selection regards the bands with the maximum determinant of the covariance matrix as the optimal band collection. By adopting TF, MEV–TF replaces the matrix determinant with scalar multiplication and achieves incremental calculation, which decreases the computational cost significantly. MEV–TF tries to select bands with large information and low correlation. Experimental results on different real data verify the efficiency of the proposed method.