This paper presents a very reliable and computationally simple algorithm to transform a two-time-scale system in the singularly perturbed form by permutation followed by scaling, assuming that certain conditions are satisfied. The algorithm is based on computing orthonormal bases which span the left and the right invariant subspaces associated with the slow eigenvalues. The algorithm does not require the system to be diagonalizable. Moreover, the algorithm works even if the original system is badly scaled. Examples are given to illustrate the proposed algorithm.