For a singular, non-causal descriptor system of order n, a (p — k)lh order observer is proposed where p =n — q, q is the number of infinite non-dynamic modes of the system and k is the rank of a matrix obtained from a transformed system derived by using the singular value decomposition. Some useful results are given which establish the existence of this observer and which resolve problems encountered with pth order observers proposed in the literature. Robustness is achieved by choosing optimum gain matrices which reduce the sensitivity of observer performance to perturbations.