With 4 s resolution data of FGM and HIA on Cluster/C1, the earthward Convective Bursty Flows (CBF) inside the region of -19 Re < x < -9 Re, -10 Re < y < 10 Re and -5 Re < z < 5 Re were statistically analyzed in the GSM coordinate. According to the statistical results, the CBF inside the Central Plasma Sheet (CPS) has distinctly ``braking'' inside 13~15 Re, and ``absence'' around 11.5 Re. The further detail analysis of the velocity of the CBF showed that the CBF move mainly toward the earth. The speed of the CBF has no clear decrease while moving earthward. In addition, the CBF have stronger perpendicular velocity inside 13 Re than outside 15 Re. This implied that the ``absence of BBF'' is not due to the deflection of the high-speed flows. The ``braking'' and ``absence'' of BBF may be closely related. The joint observations of TC-1 and Cluster satellites are important for understanding the transport process of the CBF in the CPS.