French Polynesia's opposition Tahoeraa Huiraatira party says its 11-member bloc in the assembly is firm despite one member failing to support its candidate in the presidential election.
Geffry Salmon received only 10 votes in the assembly while the incumbent Edouard Fritch secured 39 votes to be re-elected president for another five-year term.
The surprise shift is being described by the Tahoeraa's Teura Iriti as an incident, but she declined to say who voted for Mr Fritch and why.
Radio1 said it had established that it was Fernand Tahiata who failed to toe the party line.
Mr Fritch's election came after his Tapura Huiraatira Party won a landslide victory in the territorial election two weeks ago when it won two thirds of the 57 seats.
The pro-independence Tavini Huiraatira party won eight seats and in the presidential election its candidate Oscar Temaru won eight votes.
The new government is expected to be presented this week.