An exact method is presented for discretizing a constant-coefficient, non-square, matrix differential Riccati equation, whose solution is assumed to exist. The resulting discrete-time equation gives the values that have no error at discrete-time instants for any discrete-time interval. The method is based on a matrix fractional transformation, which is more general than existing ones, for linearizing the differential Riccati equation. A numerical example is presented to compare the proposed method with that based on gage invariance and bilinearization, which has better performances than the conventional forward-difference method.