The constant-speed straight-line propagation in free space is a basic characteristic of light. Recently, several novel spatiotemporal coupling methods, for example, flying focus (or named sliding focus), are developed to control light propagation including velocity and direction. In the method of flying focus, where temporal chirp and longitudinal chromatism are combined to increase the degree of freedom for coherent control, tunable-velocities and even backward-propagation have been demonstrated. Herein, we studied the transverse and longitudinal effects of the flying focus in space and time, respectively, and found in a specific physics interval existing an unusual reciprocating propagation that was quite different from the previous result. By significantly increasing the Rayleigh length in space and the temporal chirp in time, the newly created flying focus can propagate along a longitudinal axis firstly forward, secondly backward, and lastly forward again, and the longitudinal spatial resolution for a clear reciprocation flying focus improves with increasing the temporal chirp. When this new type of light is applied in the radiation pressure experiment, a reciprocating radiation-force can be produced in space-time accordingly. This finding further extends the control of light and might enable important potential applications.