"There's definitely belief that we can beat them. We know that on paper they're a very good team. They've got some experience throughout their line-up and some proven world-class players," McCullum said.
"But we are playing in our conditions, we've got what we think's a pretty exciting unit as well. Our bowlers are going very well at the moment. Our batters have done pretty well all summer led by Martin Guptill and Rob Nicol up front as well, which has been great and we know that in the field we are as good as anyone around the world. So if we can get our performance together on the day across the board then we are going to put South Africa under pressure and, in our own conditions with our home crowd behind us, we are confident we can get the job done."
South Africa have welcomed Dale Steyn, Graeme Smith, Jacques Kallis and Faf de Plessis in to their squad from the outfit who played the Twenty20s, while New Zealand have ushered in Tarun Nethula and Andy McKay to join the side who contested the 20-over format.
South African captain AB de Villiers didn't want to declare his side as favourites but felt they had more than a starters' chance.
"We are still away from home. New Zealand's a very good one-day unit. We know that; very dangerous," he said.
"We are ranked higher than them so we should be winning but it's going to be a tough series, that's for sure. I think they're hurting after that T20 series, they've also got that same look in the one-day team, not too many changes."
Tomorrow's game starts at 2pm and the bookies have the Proteas as favourites at $1.60, with New Zealand at $2.20.