In this paper, a novel solver for extracting FKT discriminant subspace was proposed. This solver extracted subspaces by solving a set of least-norm equations instead of using matrix decomposition. One gained property is that the proposed method does not rely on a large number of samples for training. This property was evidenced in experiments where a satisfied classification result was seen with only 10 training samples. Even with such a small number of training samples, the discriminant subspace extracted by the proposed method is still comparable with, if not better than, the matrix decomposition based FKT method.