Desire has begun drilling its Dawn/Jacinta 25/5-1 well in the North Falkland Basin.
The group said it expected to take about a month to drill the well and would make more announcements when appropriate.
The group’s shares soared and then tumbled earlier this month after it said it thought it had struck oil at its Rachel North well, only to have to announce later that the well contained mainly water.
Desire said it had learned lessons from the failed well and would press ahead with more exploration.
The group started the new well in its wholly-owned Tranche I in the North Falkland basin on Saturday.
Once finished, Desire will hand over the Ocean Guardian rig to another explorer, Rockhopper, which will use it before returning it to Desire to drill a well at a location still to be decided.
Controversy has dogged drilling by Desire and other UK oil firms amid opposition to their operations from the Argentinian government.