It is helpful to improve the accuracy of the flying-start-stop liquid flow calibration facilities used to calibrate different types of flowmeters by studying and decreasing the flow diverter timing error. In this paper, a transforming relationship model of diverting flow error and timing error is proposed to reveal the principle of the timing error. Meanwhile, a same directional diverter based on the transforming relationship model is also proposed, which has the following advantages: a small timing error, a high repeatability accuracy, no need to adjust the trigger position, easy to implement ISO4185 calibration test, a wide range of working flow rates, easy to be manufactured, and a good portability. To verify the advantageous characteristics of the same directional diverter, the performance comparing experiments of the same directional diverter and the traditional diverter under different flow rates, trigger positions, and diverter moving velocities are proposed. The results show that the timing error of the same directional diverter has no relationship with trigger position and has low sensitivity in both flow rate and the diverter moving velocity. While the diverter moving velocity is 0.1 m/s, the absolute value of the timing error of the same directional diverter just varies from 0.251 to 1.473 ms, which is much smaller than the traditional diverter’s (varies from 9.940 to 532.302 ms). The uncertainty caused by the timing error and the total uncertainty of measuring time of the same directional diverter vary from 0.000454% to 0.000883% and 0.000529% to 0.000924%, respectively.