For the random hopping frequency signal, the modulated frequencies are randomly distributed over given bandwidth. The randomness of modulated frequency not only improves the electronic counter countermeasure capability for radar systems, but also determines its performance of range compression. In this paper, the range ambiguity function of RHF signal is firstly derived. Then, a design method of frequency hopping pattern based on stationary phase principle to improve the peak to side-lobe ratio is proposed. Finally, the simulated experiments show a good effectiveness of the presented design method.