The local authority area produced a zero return for the week June 21-27 according to the statistics from National Records of Scotland (NRS).
It was the third such return in the past four weeks.
The last single death which mentioned COVID on the death certificate was in mid-June
The NRS confirmed that deaths across Scotland for June 21-27 period were up four from the previous week.
There were two in each of Aberdeen City, Aberdeenshire, City of Edinburgh, Clackmannanshire, East Ayrshire and Midlothian.
Dundee City, East Renfrewshire, Glasgow City, Renfrewshire and South Lanarkshire all recorded one death each.
The number of deaths from all causes registered in Scotland in this week was 1,043 - that’s 24, or 2%, more than the five year average.
Pete Whitehouse, director of statistical services, said: “The number of deaths has risen slightly in recent weeks but is still very low relative to the number of COVID-19 cases.
“Two deaths were aged under 65, five were aged 65-74 and there were ten deaths in people aged 75 or over. Four were female and thirteen were male.
“Fourteen deaths were in hospitals, three deaths were at home or in a non-institutional setting. No care home deaths were registered in week 25.”