We propose a method to improve discrimination for synthetic discrimination function (SDF), which is carried out by training the complementary samples under the condition of zero correlation peaks while the samples under the condition of equal correlation pobs. Therefore, the distances between the trained class and all other classes are increased in the decision space and high discrimination is resulted from. On the other hand, the advantage of the distortion-invariant recognition for synthetic discrimination function is kept as well. Experimental results related to fingerprint identification are given.