The All Blacks have dropped to fifth in World Rugby's rankings, their lowest spot on record.
It came after Sunday's 26-10 defeat by South Africa, their fifth loss in their past six Tests dating back to Dublin last year.
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They swap places with England in the only movement in the top 10.
It comes amid speculation about the future of head coach Ian Foster, who has made a couple of changes to his coaching line-up but remains under intense pressure due to the string of poor performances.
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