We report the eruption of a small filament on 2001 September 28. Followed by a two-ribbon flare, the eruption was associated with a partial halo coronal mass ejection. During the eruption, coronal bipolar double dimmings were formed on the regions of opposite magnetic polarities. The optical counterparts of the coronal dimmings, i.e., the $H_{\alpha}$ dimmings, were clear and showed similar appearance and consistent development. A remarkable fact is that the two dimmings were preceded by impulsive EUV and $H_{\alpha}$ brightenings at the flare's rise phase, suggesting that the eruption can be explained by the tether-cutting model.