Fund Project:the National Natural Science Foundation of China (No.10571061); the Science Foundation of Guangdong Province (No.0501332) and the Science Foundation of the Department of Education of Yunnan Province (No.07C10110).
In this paper, a complete congruence on the congruence lattice of regular semigroups with $Q$-inverse transversals is analysed. The classes of this complete congruence which are intervals are discussed and their least and greatest elements are presented clearly.