We examine variability of absorption line strength of intervening systems along the line of sight to GRB 060206 at $z = 4.05$, by the low-resolution optical spectra obtained by the Subaru telescope from six to ten hours after the burst. Strong variabilities of Feemissiontype{II} and Mgemissiontype{II} lines at $z=1.48$ during $t=$5--8 hours have been reported for this GRB citep{Hao07}, and this has been used to support the idea of clumpy Mgemissiontype{II} cloudlets that was originally proposed to explain the anomalously high incidence of Mgemissiontype{II} absorbers in GRB spectra compared with quasars . However, our spectra with higher signal-to-noise ratio do not show any evidence for variability in $t=$6-10 hours. There is a clear discrepancy between our data and Hao et al. data in the overlapping time interval. Furthermore, the line strengths in our data are in good agreement with those observed at $t sim$ 2 hours by citet{Tho08}. We also detected Feemissiontype{II} and Mgemissiontype{II} absorption lines for a system at $z = 2.26$, and these lines do not show evidence for variability either. Therefore we conclude that there is no strong evidence for variability of intervening absorption lines toward GRB 060206, significantly weakening the support to the Mgemissiontype{II} cloudlet hypothe sis by the GRB 060206 data.
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