Statistics show there were 2,400 fewer patients attending accident and emergency in the second week of the year than the previous week.
Waiting time figures showed 85.8 per cent of patients attending A&E were dealt with within the four-hour target time.
This was up from 77.9 per cent in the first week of the year and 78 per cent in the run-up to Hogmanay.
Figures showed there were 22,883 attendances at A&E, the lowest figure since exactly a year ago, when 90 per cent were seen within the target time.
The latest stats showed 552 patients spent more than eight hours in an emergency department and 118 were there for more than 12 hours, both down on the previous week.
The flu rate for the start of the year was five times higher than the same time last year, putting pressure on A&E.
The latest Health Protection Statistics, covering the same period as the A&E figures, said the rate was 114 people per 100,000 reporting a flu-like illness in the week to 14 January.
However, health experts believed the flu rate peaked around this time.
The Scottish government’s A&E target is for 95 per cent of patients to be admitted, discharged or transferred within four hours.
Health Secretary Shona Robison said: “Our A&E departments are continuing to be impacted by the pressures and demand of winter, so these improving statistics are a really significant achievement.
“Flu rates in Scotland are currently almost five times higher than the same period last year and hospitals are reporting a high number of people with already-significant care needs contracting flu, which is increasing demand even further.
“We still have a few months of winter left and there’s no doubt we’ve still got some challenging weeks ahead, particularly with the bad weather we’re experiencing, but I’d like to say than you once again to health staff right across Scotland for their continued dedication and hard work.”
Clinicians are encouraging those in eligible groups to protect themselves and their families by getting the vaccine. The current predominant strain is still is covered by this year’s flu vaccine.
Deputy Chief Medical Officer, Dr Gregor Smith, said: “The volume of flu cases and already-ill patients contracting flu-like illness is continuing to put strain on systems and it is crucial that patients with complex care needs and flu receive the right care, not simply the fastest.
“I would continue to encourage anyone in an eligible group to get vaccinated - it is the best defence against flu.”
Labour health spokesperson Anas Sarwar said: “While this is a welcome improvement on last week, the reality is the first fortnight of 2018 has been incredibly challenging for our health service.
“Almost 9,000 patients have waited longer than the 4-hour standard the SNP set our NHS, and more than 2,000 have waited over 8 hours. These are staggering figures for a two-week period.
“NHS staff are not getting the support they need from the SNP government in Edinburgh.
“That’s why Labour is the only party to set up a workforce commission to tackle the staffing crisis in our NHS. The health service needs more than sticking plaster solutions. It needs a plan for long term real change.”