It's believed that the working relationship between NZF technical director Andy Boyens and Schmid has been less than ideal in recent months, with some differences in philosophy on how to proceed forward with New Zealand's men's national teams.
However NZF CEO Andrew Pragnell stressed it was a unilateral decision from Schmid.
"It is his decision rather than a discussion," Pragnell told the Herald. "I've been talking with Fritz a bit this week but ultimately the decision is his, totally. We had some private conversations and he is heading back to Switzerland. That's as far as we go. We respect that and it is up to us now to look towards the future."
Pragnell didn't think there were issues between Boyens and Schmid.
"I don't believe so," said Pragnell. "There is always healthy office debate — led by everyone really — but I don't think so. Relationships are positive internally and externally."
Pragnell also wouldn't discuss the amount of any settlement with Schmid, or indeed if there had been one, saying he couldn't go into private employment or contract related matters.
Schmid was appointed in February 2018. That decision was clouded in some controversy, given his close association with former NZF technical director Andreas Heraf, who drove the appointment process.
The All Whites haven't played since June last year, at a four team tournament in India. Their next international is scheduled for November, against Ireland.
Their lack of international match play must have been a source of ongoing frustration for the 59-year-old, who even used contacts to try to arrange games himself during a FIFA window earlier this year, but he was positive in a statement.
"I am extremely grateful for my experience at the helm of the All Whites," said Schmid. "I have met countless members of the New Zealand football community, who received me with great respect and true open-mindedness. I would like to thank all of them for their trust and support during my time at NZF. My special thanks goes to my coaching staff and, most of all, to our players: thank you for granting me the privilege of working with you."
Pragnell said the immediate priority was to appoint an interim coach for the New Zealand team at next month's Pacific Games, before commencing a "robust, detailed" recruitment process for the All Whites position.
