The patient, who is understood to have died in the last 24 hours, was said to have significant underlying health problems.

Ms Sturgeon said, “My deepest sympathy is with the patient’s family and friends. I continue to urge all those in the at-risk groups to take up the vaccine invitation from their GPs.”

The Health Secretary said, however, that a further drop in the swine flu cases this week was an encouraging sign that the vaccination programme was having the desired effect.

“The vast majority of those who contract H1N1 will experience relatively mild symptoms and make a full recovery,” she said.

NHS Tayside today declined to release further information about the death.

A spokeswoman for the Scottish Government was unable to give details of the age or sex of the victim, or he or she had lived.

The latest swine flu report by Health Protection Scotland shows that 104 people have been treated in hospital in Tayside since the beginning of the outbreak.

By December 14, six patients had required treatment in intensive care and a further two were cared for in high-dependency units.

The remainder displayed milder symptoms and were cared for in general wards.

Only yesterday, Ms Sturgeon warned that Scotland could be hit by a third wave of swine flu in the New Year.

She said indications were that the second wave of the outbreak was now in decline, adding that “significant” numbers of people had now been vaccinated.

Anyone concerned about flu-like symptoms should continue to contact their GP for advice, or NHS 24 on 08454 24 24 24. Further information on the vaccine programme is available via the new Scottish Swine Flu Vaccination Helpline on 08000 28 28 16.