  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.
