The Hermes experiment studies the spin structure of the nucleon using the 27.6 GeV longitudinally polarized positron beam of HERA and an internal target of pure gases. Recently Hermes presented preliminary result on the deuteron spin structure function gd_1 in the kinematic range 0.002<x<0.85 and 0.1<Q2<20GeV2 based on a restricted data set. Here, new, precise results are presented using the superior statistics of the 2000 data taking period. A reduction of the systematic uncertainty which could be achieved in this preliminary analysis relies in particular on the excellent performance of HERA and of the HERMES target.