The conjugate flows over a step with the height h0, which might be positive or negative, was studied in a three-layer fluid and the coupled nonlinear equations were derived, with which the effects of varying height h0 on the existence and evolution of conjugate flows were examined. It is concluded that the conjugate flow is sharply sensitive to the thickness of fluid layers and its characteristics alters remarkably due to the existence of the step. As the flow climbs up a step (h0＞0), the conjugate flow with a convex lower interface and a concave upper interface is allowed to appear, while the flow with the concave lower interface or the simultaneous concave interfaces will be depressed. As the flow goes down a step (i.e., h0＜0), on most occasions only one kind of conjugate flow could exist, which prossesses the form with the simultaneous convex interfaces and will disappear rapidly with the increase of the step depth.