||For the two classes supervised learning problem, we present a refinement method for increasing the classification accuracy of an initial separating hyperplane in the feature space Rd. The main idea corresponds to dimensionality reduction of, e.g. LDA separation, however not in its original form Rd → R but rather as dimensionality reduction Rd → Rj for some j < d and j > 1. The method combines discriminant and margin-based properties of the separation. Due to efficiency reasons, we define rules for fast calculation of the refinement. Furthermore, we discuss theoretical fundamentals of our method and show its high performance by cross-validation tests on datasets from the UCI Machine Learning Repository with different numbers of features and objects. Due to the margin-based origin, the method is suitable for not well-balanced datasets. Cross-validation tests for not well-balanced data are given as well.