The kernel trick – commonly used in machine learning and computer vision – enables learning of non-linear decision functions without having to explicitly map the original data to a high dimensional space. However, at test time, it requires evaluating the kernel with each one of the support vectors, which is time consuming. In this paper, we propose a novel approach for learning non-linear SVM corresponding to the histogram intersection kernel without using the kernel trick. We formulate the exact non-linear problem in the original space and show how to perform classification directly in this space. The learnt classifier incorporates non-linearity while maintaining O(d) testing complexity (for d-dimensional input space), compared to O(d Nsv) when using the kernel trick. We show that the SVM problem with histogram intersection kernel is quasi-convex in input space and outline an iterative algorithm to solve it. The proposed approach has been validated in experiments where it is compared with other linear SVM-based methods, showing that the proposed method achieves similar or better performance at lower computational and memory costs.