Desire has announced that despite drilling to a depth of 1,300m at its Jacinta well in the North Falkland basin, there were no hydrocarbons.
The company's shares fell 29% on the news, despite Desire saying that it would now drill to 1,670m.
On 6 December, Desire's shares tumbled 50% after another well was capped.
Desire's shares, which reached 170p in October, closed down 29.4% at 42.5p.
When exploration off the Falklands began earlier this year, the share prices of several companies rose in expectation of an oil and gas boom.
But analysts say drilling results have so far proved disappointing.
And in November there were reports that ExxonMobil, the world's largest oil company not owned by a government, had decided that the islands contained insufficient hydrocarbons to make exploration profitable.
Shares in Desire Petroleum have again fallen sharply after another disappointment over the firm's oil exploration off the Falkland Islands.