We present a new method, called hyperplane folding, that increases the margin in Support Vector Machines (SVMs). Based on the location of the support vectors, the method splits the dataset into two parts, rotates one part of the dataset and then merges the two parts again. This procedure increases the margin as long as the margin is smaller than half of the shortest distance between any pair of data points from the two different classes. We provide an algorithm for the general case with n-dimensional data points. A small experiment with three folding iterations on 3-dimensional data points with non-linear relations shows that the margin does indeed increase and that the accuracy improves with a larger margin. The method can use any standard SVM implementation plus some basic manipulation of the data points, i.e., splitting, rotating and merging. Hyperplane folding also increases the interpretability of the data. © 2019 Association for Computing Machinery.