Supersymmetric Matrix Quantum Mechanics with Non-Singlet Sector

We consider a supersymmetric matrix model which is related to the non-critical superstring theory. We find new non-singlet terms in the supersymmetric matrix quantum mechanics. The new non-singlet terms give rise to nontrivial interactions. These new non-singlet terms from fermions, can eliminate other non-singlet terms from generators of U(N) subalgebra and from time periodicity. The non-singlet terms from the generators violate the T-duality on the target space which is a circle. Therefore, we can retain the T-duality with a process of the elimination.