High-order accurate schemes are employed to numerically simulate the interaction of a supersonic jet and a co-directional supersonic inflow. A double backward-facing step model is proposed to investigate the interaction between the jet shear layer and the supersonic inflow shear layer. It is found that due to the interaction of the shear layer, a secondary jet is injected into the recirculation zone at the intersection of the two shear layers. The secondary jet produced by the interaction of the two shear layers has a periodicity because of shear layers interaction. The distinction in the shape of double backward-facing steps will induce changes in the period of the secondary jet. The analysis and discussion of the periodicity of the secondary jet are mainly focused in this letter.