Few band selection methods are specially designed for small target detection. It is well known that the information of small targets is most likely contained in non-Gaussian bands, where small targets are more easily separated from the background. On the other hand, correlation of band set also plays an important role in the small target detection. When the selected bands are highly correlated, it will be unbeneficial for the subsequent detection. However, the existing non-Gaussianity-based band selection methods have not taken the correlation of bands into account, which generally result in high correlation of obtained bands. In this paper, combining the third-order (third-order tensor) and second-order (correlation) statistics of bands, we define a new concept, named joint skewness, for multivariate data. Moreover, we also propose an easy-to-implement approach to estimate this index based on high-order singular value decomposition (HOSVD). Based on the definition of joint skewness, we present an unsupervised band selection for small target detection for hyperspectral data, named joint skewness band selection (JSBS). The evaluation results demonstrate that the bands selected by JSBS are very effective in terms of small target detection.