One Nation has lost a member in the Senate after the man replacing Malcolm Roberts - Queensland publican Fraser Anning - quit the party on his first morning on the job.

Party leader Pauline Hanson issued a press release on Monday confirming Senator Anning had "abandoned" the party to stand as an independent.

The move comes after weeks of behind-the-scenes friction between Senator Hanson - a strong backer of Mr Roberts - and members of Mr Anning's incoming staff.

Senior former staffers for Mr Roberts are now on Senator Anning's staff - and have been working with him for some time, including while Mr Roberts was still a senator.