Flinders was promoted to commander in February 1801, and was selected to command H.M.S. Investigator, a vessel over 334 tons. The Admiralty gave him the the task to explore, in detail, among other places, that part of the south Australian coastline, then referred to as 'the Unknown Coast'.
In April 1801 he had married Ann Chappelle of Lincolnshire hoping to take her with him on his voyage. However, the Admiralty refused to permit it and therefore it would they would be 9 years before they would be reunited.
He reached Cape Leeuwin, southern Western Australia, late in 1801 after a passage which demonstrated his ability as a navigator and his attention to the welfare and health of his crew. Flinders set about mapping Australia’s ‘Unknown Coast’.
His precise, detailed maps are the result of his methodical practice of personally taking all bearings and returning each day to where the previous day’s work had ended.
The Investigator was resupplied and refitted in Sydney in May 1802, before Flinders began his circumnavigation of the continent, accompanied by an Aboriginal translator, Bungaree.
But the vessel was leaking badly as it reached the Gulf of Carpentaria. Flinders abandoned the charting work, but continued the circumnavigation to Sydney, limping back into port in June 1803.