Mr Costello also ignored Mr Howard's weekend direction against personal attacks on Mr Latham by suggesting the Opposition Leader should have been dumped after a 'drunken' incident involving a Sydney cab driver two years ago.
He suggested Mr Latham was taking a hypocritical stance over Democrat leader Andrew Bartlett's drunken accosting last week of Liberal Senator Jeannie Ferris.
'Well, Andrew Bartlett gets drunk and assaults someone and he is compelled to stand aside,' Mr Costello said.
'Another person gets drunk, has a fight over property and assaults someone and they make him party leader.'
He added: 'I heard Mr Latham said yesterday that he would sack a frontbencher that behaved like that.
'Well, which frontbencher do you think he might have had in mind? Himself?'
Mr Howard was forced at the weekend to pull the Health Minister, Tony Abbott, into line after he attacked Mr Latham in Parliament over his first marriage.
Costello's allegation is untrue. Latham was not charged with assault. The police investigated. Latham said he was defending himself from an attempted robbery. The police laid no charges. Trying to draw a moral equivalence between Latham and Bartlett is drawing a very long, and very dishonest bow.
Generational change seems to be generating a certain instability within the Liberal Party.