Band Selection (BS) is a long-term topic in the field of remote sensing. Among many types of BS algorithms, a branch, called band subset selection (BSS) is the one which is more suitable to find the global optimal solution. This paper presents a simple and efficient BSS method for hypesrspectral imagery. Firstly, it uses two efficient iterative ways originated from a well-known endmember extraction algorithm to search the band subset. Secondly, to evaluate the degree of informative complementary of each band subset under the iteration, we use self-sparse model to measure the similarity between the currently selected band subset and full bands, where the sparse coefficient can be efficiently solved by using the least square formula. We call this method self-sparse-based BSS (SSpaBSS). Unlike the existing BS approaches which may only find the locally optimal solution by a single search path, the SSpaBSS can find the nearly globally optimal solution. The experiments conducted on a real hyperspectral dataset demonstrate that the proposed SSpaBSS can find appropriate band subsets for land cover classification.