A Liberal MP crossed the floor to support Indi MP Helen Haines' bill to establish an integrity commission, but it was not debated on Thursday.
Tasmanian MP Bridget Archer voted with Dr Haines, crossbench members, Labor and the Greens to suspend standing orders to allow the bill to be debated.
"Today in the House of Representatives 66 members of integrity, of conviction, voted in favour of debating my bill for the Australian Federal Integrity Commission," Dr Haines said.
"That is more than voted against it.
"It is only because of a technicality in the standing orders that calls for an absolute majority that it was lost.
"This section of the standing orders is undemocratic during the pandemic and should be changed."
Dr Haines said "we have waited too long for a federal integrity commission".
"The Government must allow my bill for an Australian Federal Integrity Commission to be debated and I am confident it will pass," she said.