We present a method to find the exact maximal margin hyperplane for linear Support Vector Machines when a new (existing) component is added (removed) to (from) the inner product. The maximal margin hyperplane with the new inner product is obtained in terms of that for the old inner product, without re-computing it from scratch and the procedure is reversible. An algorithm to implement the proposed method is presented, which avoids matrix inversions from scratch. Among the possible applications, we find feature selection and the design of kernels out of similarity measures.