The coding gain in subband coding, a popular technique for achieving signal compression, depends on how the input signal spectrum is decomposed into subbands. The optimality of such decomposition is conventionally addressed by designing appropriate filter banks. In this paper, the issue of optimal decomposition of the input signal spectrum is addressed by choosing the set of band edges that, for a given number of bands, will achieve maximum coding gain. A set of necessary conditions for such optimality is derived, and an algorithm to determine the optimal band edges is then proposed. These band edges, along with ideal filters, achieve the upper bound of coding gain for a given number of bands. It is shown that with ideal filters, as well as with realizable filters for some given effective length, such a decomposition system performs better than the conventional non-uniform binary tree-structured decomposition in some cases for AR sources as well as images.