For the descriptor system Ex = Ax + Bu, y = Cx + Du, an observer of the order p = rank E - p1 (0 less-than-or-equal-to p1 less-than-or-equal-to rank E) is developed. It is not assumed that the descriptor systems are necessarily regular. The derivation is straightforward using only an algebraic approach. The existence conditions of the observer are also presented. These conditions are less restrictive than existing ones. Some illustrative examples are included.