The proposed work aims at proposing a alternative kernel decomposition in the context of kernel machines with indefinite kernels. The original paper of KSVM (SVM in Kre˘ ın spaces) uses the eigen-decomposition, our proposition avoids this decompostion. We explain how it can help in designing an algorithm that won't require to compute the full kernel matrix. Finally we illustrate the good behavior of the proposed method compared to KSVM.