Prime Minister Junichiro Koizumi's chances for re-election as chief of the ruling Liberal Democratic Party have gotten even better, with another major intraparty faction moving to allow its members to decide who to vote for in the Sept. 20 race.

The 51-member faction led by party Executive Council Chairman Mitsuo Horiuchi gave up Friday on forming a consensus among its members on who to support.

Horiuchi had earlier said he will vote for Koizumi, and some other members are expected to follow suit.