We propose a method of modifying a kernel function to improve the performance of a support vector machine classifier. This is based on the structure of the Riemannian geometry induced by the kernel function. The idea is to enlarge the spatial resolution around the separating boundary surface, by a conformal mapping, such that the separability between classes is increased. Examples are given specifically for modifying Gaussian Radial Basis Function kernels. Simulation results for both artificial and real data show remarkable improvement of generalization errors, supporting our idea.