The man, 35, from Vista in Adelaide, died on Friday in a workplace accident at the desalination plant construction site at Lonsdale in Adelaide's southern suburbs.

A full safety audit of the site on Thursday by the federal Safety Commission gave a green light to operations just a day before the accident.

The Construction, Forestry, Mining and Energy Union (CFMEU) has said the audit was "a lot of paper work pushed around the place".

CFMEU SA secretary Martin O'Malley said the union will conduct its own audit, only "we'll do it properly".

"This is a response to a fatality in the industry, this will be done properly," he said yesterday.

The union has already called for the use of soft slings to be banned on construction sites, blaming the misuse of the slings as directly responsible for the fatality on Friday.

Work on the site is unlikely to continue before Thursday at the earliest but Mr O'Malley said he expects some workers may not return due to ongoing safety concerns.

Previous concerns had been raised about the timetable for the construction.

"It's all about urgency," said Mr O'Malley.

The desalination plant, which will eventually provide up to half of Adelaide's water supplies, is due to start operating later this year.