Australia's best-known whale, Migaloo, appears to have turned up again. But not where he usually does.

The big white humpback is normally found cruising up the eastern Australian coastline at this time of year. Instead, New Zealand scientists are virtually certain they have recorded him in Cook Strait.

The distinctive dorsal fin, spine and colour of Migaloo, in Cook Strait. The yellow film on the skin is diatom algae. Credit:Department of Conservation, NZ

The colour, distinctive "crooked finger" dorsal fin, and prominent spine, strongly indicate that it is Migaloo, Nadine Bott, of the New Zealand Department of Conservation, says.

"White humpbacks are extremely rare," Ms Bott said. "Only four have been reported in the world."