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In New Zealander Cotter's first home match in charge, Scotland beat Argentina 41-31 and, encouragingly, scored five tries in the process.
But no Scotland side has ever beaten New Zealand in 29 attempts dating back to 1905, with the last of their two draws with the All Blacks a 25-25 share of the spoils at Murrayfield back in 1983.
Greig Laidlaw - man of the match against the Pumas - continues to captain the team from scrumhalf, while the New Zealand-born duo of wing Sean Maitland and back-row Blair Cowan will face the All Blacks for the first time in a Test match.
Cotter has though made four changes on his bench, with Glasgow Warriors forwards Fraser Brown (hooker) and Tim Swinson (lock) replacing Scott Lawson and Jim Hamilton - who spent just four minutes on the field against Argentina before being sin-binned - while Johnnie Beattie and Chris Cusiter have come in for Alasdair Strokosch and the injured Henry Pyrgos (head knock).
"Last weekend we had the ball and looked dangerous, and showed great character to keep faith and confidence in our attacking philosophy," said Cotter in a Scottish Rugby Union statement.
"I really enjoyed watching the players play for each other against Argentina.
"They picked themselves up time and time again, and encouraged each other to keep on working for our collective cause.
"It was fantastic to see, as was our ability to get over the line and score tries, all of which contributed to a strong case for reselection."
He added: "We showed last weekend that we're developing an attack than can cause opposition teams problems. If we can force the All Blacks into making errors then we can give ourselves a chance.
"In saying that, the All Blacks are the world's best at exposing errors so we'll also have to be absolutely clinical in both our decision-making and execution if we are to go one better than the 1983 team that drew with New Zealand here at Murrayfield."
Teams:
Scotland
15 Stuart Hogg, 14 Sean Maitland, 13 Mark Bennett, 12 Alex Dunbar, 11 Tommy Seymour, 10 Finn Russell, 9 Greig Laidlaw (captain), 8 Adam Ashe, 7 Blair Cowan, 6 Rob Harley, 5 Jonny Gray, 4 Richie Gray, 3 Euan Murray, 2 Ross Ford, 1 Alastair Dickinson
Substitutes: 16 Fraser Brown, 17 Gordon Reid, 18 Geoff Cross, 19 Tim Swinson, 20 Johnnie Beattie, 21 Chris Cusiter, 22 Duncan Weir, 23 Sean Lamont
New Zealand
Substitutes: 16 Dane Coles, 17 Wyatt Crockett, 18 Ben Franks, 19 Luke Romano, 20 Liam Messam, 21 Augustine Pulu, 22 Sonny Bill Williams, 23 Julian Savea
