We report new follow-up spectroscopy of i′-dropout galaxies with an NB921-band depression found in the Subaru Deep Field. The NB921-depressed 1′-dropout selection method is expected to select galaxies with large equivalent-width Lyα emission over a wide redshift range, 6.0 ≲ z ≲ 6.5. Two of four observed targets show a strong emission line with a clear asymmetric profile, identified as Lyα emitters at z = 6.11 and 6.00. Their rest-frame equivalent widths are 153 Å and 114 Å, which are lower limits on the intrinsic equivalent widths. Through our spectroscopic observations (including previous ones) of NB921 -depressed i′-dropout galaxies, we identified 5 galaxies in total with a rest-frame equivalent width larger than 100 Å at 6.0 ≲ z ≲ 6.5 out of 8 photometric candidates, which suggests that the NB921 -depressed i′-dropout selection method is possibly an efficient way to search for Lyα emitters with a large Lyα equivalent width, in a wider redshift range than with usual narrow-band excess techniques. By combining these findings with our previous observational results, we infer that the fraction of broad-band selected galaxies having a rest-frame equivalent width larger than 100 Å is significantly higher at z ∼ 6 (the cosmic age of ∼1 Gyr) than that at z ∼ 3 (∼2 Gyr), being consistent with the idea that the typical stellar population of galaxies is significantly younger at z ∼ 6 than that at z ∼ 3. The NB921-depressed i′-dropout galaxies may be interesting candidates for hosts of massive, zero-metallicity Population III stars. © ESO 2007.