The large level limit of the N = 2 SO(2N ) Kazama-Suzuki coset models is argued to be equivalent to the orbifold of 4N free fermions and bosons by the Lie group SO(2N ) × SO(2). In particular, it is shown that the untwisted sector of the continuous orbifold accounts for a certain closed subsector of the coset theory. Furthermore, the ground states of the twisted sectors are identified with specific coset representations, and this identification is checked by various independent arguments.