While the fledgling government has been backed by two court decisions so far, Timothy Benga is launching his own challenge after losing the forestry ministerial portfolio to former Opposition Leader Belden Namah, who was also appointed deputy prime minister.
According to the ABC, Bonga will argue that the position of prime minister was not vacant when parliament voted on the successor to Sir Michael Somare.
Former Treasurer Peter O'Neill received 70 votes compared to 24 for acting Prime Minister Sam Abal for the top job in the widely reported vote last week.
Ousted Attorney-General Sir Arnold Amet's bid to dispute this election of O'Neill as unconstitutional failed last week when the Supreme Court reportedly decided he had no legal standing.
Abal also lost his attempt to seek an injunction on similar grounds when his application was dismissed by National Court Judge Gavara-Nanu on Friday.
Key new appointments
William Duma has regained his role as petroleum and energy minister, while John Pundari has been replaced by Byron Chan as mining minister.
One industry observer could not recount to PNGIndustryNews.net if Byron, the son of former Prime Minister Sir Julius Chan, had any previous exposure to the nation's mining industry.
While Sir Puka Temu was well regarded as a mining minister before he fell out with the Somare government and lost the role, he has been appointed as the agriculture and livestock minister.
Sam Basil, who criticised environmental matters around the Hidden Valley gold mine earlier this year, was appointed as the national planning minister.
Don Poyle - who recently replaced Somare as National Alliance leader, according to The National - was appointed as PNG's new treasurer.
Often vocally opposed to corruption, former PNG Prime Minister Sir Mekere Morauta is the new public enterprises minister.
This important position is responsible for the Independent Public Business Corporation, which owns a 16.6% stake in the PNG LNG project on behalf of the national government.
Arthur Somare, son of Sir Michael, used to hold this post until he was suspended by a leadership tribunal.
He is facing allegations of failing to submit financial statements for several years, and for misapplying electoral funding.
The official cabinet listing, which features many first time ministers, can be downloaded as a word document by clicking the relevant document under "related links" to the right of your screen.
