A statement issued by ANZ this afternoon said that the former employee, Patrick O'Connor, has decided to "discontinue his legal action against ANZ".
"No payment will be made by ANZ to Mr O'Connor and each party will meet their own legal costs," the statement said.
Last week, ANZ defended its name after two sacked employees filed lawsuits against the bank.
In a statement, ANZ chief risk officer Nigel Williams said former traders Mr O'Connor and Etienne Alexiou were dismissed in 2015 for serious breaches of the bank's code of conduct, policies, and values
ANZ emphasised that it was committed to taking disciplinary action where it finds instances of "unacceptable" behaviour.
"This includes an uncompromising stance with former employees where the bank considers legal disputes instigated by them to be without merit," the bank said.
An ANZ spokesperson told ifa that he "presumed" Mr Alexiou was continuing with his claim.
Fairfax Media reported that the pair was suing the bank for tens of millions of dollars in damages, lost bonuses and income, saying they were exposed to inappropriate behaviour condoned by senior staff on the dealing floor.
Mr Williams said ANZ would be "vigorously" defending itself against these claims.
"All matters raised have either been investigated or are under current investigation. We have already identified that many of the allegations made in both claims are not accurate and these inaccuracies will become apparent as the matters proceed through the court system," he said.
"We have more than 1,000 staff in our global markets business in total who are working responsibly in line with our values and our code of conduct. These staff members work hard for our customers and they are highly valued contributors."
According to the statement, Mr O'Connor's dismissal was related to company-issued credit card abuse while he and Mr Alexiou both engaged in "highly inappropriate and offensive electronic communication".
Allegations made about some existing and former ANZ staff will be investigated, Mr Williams said, and action has already been taken to improve the division's conduct.
"Mr O'Connor and Mr Alexiou's claims are difficult to read for all of us at ANZ but common sense says their behaviours are not consistent with our Code of Conduct and cannot be tolerated," Mr Williams said.
"We want to be known as a bank with a strong focus on culture, ethics and fairness that our staff and customers can be proud of. We will continue to take the appropriate action to support and build our reputation for corporate responsibility."
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