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But, without criticising Mr Koizumi's trips to the shrine, Mr Machimura now says he may stop his own.
ECONOMIST: Japan
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Mr Koizumi's annual visits to the shrine have infuriated Japan's neighbours, and Mr Machimura likes to go there too.
ECONOMIST: Japan
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Those special advisers must get along with the new foreign minister, Nobutaka Machimura, who may not be content just to run the bureaucracy and make nice speeches.
ECONOMIST: Japan
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Three other candidates contested the leadership - Nobuteru Ishihara, son of Tokyo Governor Shintaro Ishihara, Nobutaka Machimura, the former foreign minister, and Yoshimasa Hayashi, another former defence minister.
BBC: Japan ex-PM Shinzo Abe elected opposition leader
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Nobutaka Machimura, the leader of the biggest faction, who had served for a month as Mr Abe's foreign minister, becomes Mr Fukuda's chief cabinet secretary and in effect government gatekeeper.
ECONOMIST: Japan's new prime minister