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The technology giant has been under fire for the past two weeks after it emailed the accused man’s name to Kiwi internet users last week.
An email was sent to anyone signed up to its “what’s trending in New Zealand” service, despite the 26-year-old man being granted name suppression by a district court judge.
Andrew Little said tonight they had a "constructive discussion" and Google has indicated to see what they can do with their systems to prevent another suppression breach like this occurring again.
Grace Millane had only just arrived in New Zealand as part of her OE and was last seen alive going into a central Auckland hotel on December 1, the day before her 22nd birthday.
The 22-year-old's body was eventually found in bush on the side of Scenic Drive in the Waitākere Ranges a week later.
Google representative Ross Young said today they understand New Zealand law and have acted on the situation.
"Google does receive court orders, including suppression orders," he said.
Young said they received the Millane court order on Friday, December 14, following the accused's court appearance on Monday.
Little said he had to defend the integrity of New Zealand's justice systems and the meeting with Google addressed this.
Google said they would look at their systems in order to ensure another breach would not take place again.
The Minister will meet with Google in the new year to discuss how they are getting on resolving the issue.
Meanwhile, Little said New Zealand media were unethical to name the Australian Catholic priest currently under trial following Google's breach.
At the end of the day, Little said if Google want to operate in New Zealand it had to comply with our laws.
The minister had already rebuked UK media for naming the accused in the Grace Millane case and said Google stepped over the line as well.
More than 100,000 searches of the the accused's name were also made following his court appearance, according to the email Google sent out.
The Silicon Valley company’s publicly available analytics also showed the accused’s name was the second-most searched item in New Zealand with more than 50,000 searches.
A Google spokesperson told The New Zealand Herald that its trends alerts were automatically generated by its algorithms and are based on searches over a time period in a selected geography.