This article proposes computationally tractable, easy to expand and tight relative gain variation bound for uncertain systems. The proposed bound is a further development of previous work, which is summarized and discussed. Using several examples, the new method is compared with previous results and the advantages are highlighted. The prediction of sign changes in relative gain array elements due to uncertainties is important for pairing decisions. Based on the proposed bound, a method for the prediction of the uncertainty levels which render sign changes is suggested. The prediction method is currently limited to certain classes of systems. In this prediction method neither prior knowledge of the uncertainty nor numerous calculations are needed.