Liberal Senator Cory Bernardi is set to defy Prime Minister Tony Abbott and co-sponsor a bill aimed at changing the Racial Discrimination Act, which the government abandoned just over a week ago.

Family First Senator Bob Day is planning to introduce a compromise bill, which will simply strike out the words "offend and insult" from the legislation rather than entirely overhaul the section as the government has proposed.

That proposal aims to make it no longer an offence to "offend" or "insult" someone on the grounds of his or her ethnicity. The Coalition pledged to reform the act after News Corp columnist Andrew Bolt was found to have breached the legislation in 2011.

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