We present an analysis of the variability of broad absorption lines (BALs) in a quasar SDSS J141955.26+522741.1 at $z=2.145$ with 72 observations from the Sloan Digital Sky Survey Data Release 16 (SDSS DR16). The strong correlation between the equivalent widths of BAL and the continuum luminosity, reveals that the variation of BAL trough is dominated by the photoionization. The photoionization model predicts that when the time interval $Delta T$ between two observations is longer than the recombination timescale $t_{rm rec}$, the BAL variations can be detected. This can be characterized as a sharp rise in the detection rate of BAL variation at $Delta T=t_{rm rec}$. For the first time, we detect such a sharp rise signature in the detection rate of BAL variations. As a result, we propose that the $t_{rm rec}$ can be obtained from the sharp rise of the detection rate of BAL variation. It is worth mentioning that the BAL variations are detected at the time-intervals less than the $t_{rm rec}$ for half an order of magnitude in two individual troughs. This result indicates that there may be multiple components with different $t_{rm rec}$ but the same velocity in an individual trough.
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