Rainbow is a very effective multivariate digital signature scheme proposed by J. Ding and D. Schmidt. In this paper, we define any scheme that has basic multilayer Rainbow structure as Rainbow-like scheme. Then, we propose a way to enhance Rainbow-like schemes’ security level against MinRank attack. In our construction, we simply turn some of their first layers’ Oil variables into Vinegar variables by adding corresponding quadratic terms. Copyright © 2014 John Wiley & Sons, Ltd.