This paper presents an approach to band selection fusion (BSF) which fuses bands produced by a set of different band selection (BS) methods for a given number of bands to be selected, nBS. Since each BS method has its own merit in finding the desired bands, various BS methods produce different band subsets with the same nBS. In order to take advantage of these different band subsets, the proposed BSF is performed by first finding the union of all band subsets produced by a set of BS methods as a joint band subset (JBS). Due to the fact that a band selected by one BS method in JBS may be also selected by other BS methods, in this case each band in JBS is prioritized by the frequency of the band appearing in the band subsets to be fused. Such frequency is then used to calculate the priority probability of this particular band in the JBS. Because the JBS is obtained by taking the union of all band subsets, the number of bands in the JBS is at least equal to or greater than nBS. So, there may be more than nBS bands, in which case, BSF uses the frequency-calculated priority probabilities to select nBS bands from JBS. Two versions of BSF, called progressive BSF and simultaneous BSF, are developed for this purpose. Of particular interest is that BSF can prioritize bands without band de-correlation, which has been a major issue in many BS methods using band prioritization as a criterion to select bands.