In recent years, some new classes of MDS self-dual codes were construed. The method is to obtain new structure by generalized GRS codes. In this paper, our idea is to construct MDS self-dual codes of length n where is composed with two subgroups of Fq. In particular, these two subgroups do not intersect. Several classes of new q-ary MDS self-dual codes under specific conditions are given by considering the intervalof s, t.