Burau representation of the braid group, Bn, has been proved to be faithful for n≤3 and unfaithful for n≥5; whereas the case n=4 remains open. On the other hand, the question of faithfulness of Gassner representation of the pure braid group, Pn , is still open for n≥4. For any n≥4, T. Chuna specified a family of new non-trivial elements in the kernel of the evaluated Burau representation at mth root of unity, where m∈N*−{3}. Along the same lines as Chuna's work, we find, for n≥4, a family of new non-trivial elements in the kernel of the evaluated Gassner representation at mth root of unity, where m∈N*−{3}. This result may possibly be a road toward answering the open question of the faithfulness of Gassner representation.