We demonstrate the trajectory measurement of the single neutral atoms deterministically using a high-finesse optical micro-cavity. Single atom strongly couples to the high-order transverse vacuum TEM_{10} mode, instead of the usual TEM_{00} mode, and the parameter of the system is (g_{10},kappa ,gamma )=2pi times (20.5,2.6,2.6)MHz. The atoms simply fall down freely from the magneto-optic trap into the cavity modes and the trajectories of the single atoms are linear. The transmission spectrums of atoms passing through the TEM10 mode are detected by a single photon counting modules and well fitted. Thanks to the tilted cavity transverse TEM10 mode, which is inclined to the vertical direction about 45 degrees and it helps us, for the first time, to eliminate the degenerate trajectory of the single atom falling through the cavity and get the unique atom trajectory. Atom position with high precision of 0.1{mu}m in the off-axis direction (axis y) is obtained, and the spatial resolution of 5.6{mu}m is achieved in time of 10{mu}s along the vertical direction (axis x). The average velocity of the atoms is also measured from the atom transits, which determines the temperature of the atoms in magneto-optic trap, 186{mu}K {pm} 19{mu}K.
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