At around 4.15pm on Friday, June 17, a silver Suzuki Ignis was involved in a collision on the B6350 Cornhill to Kelso road close to Redden Farm, between Carham and Sprouston.
The vehicle, which was travelling west, lost control on a bend causing it to overturn and collide with a fence.
Michelle Bennett, aged 47, from Berwick-upon-Tweed, who was sitting in the rear of the vehicle, was pronounced dead at the scene.
Another female passenger was taken by air ambulance to the Royal Infirmary of Edinburgh for treatment where she remains in a serious but stable condition.
Meanwhile, the female driver and a further two passengers, a man and a woman, were taken to the Borders General Hospital. Their injuries are not thought to be life threatening.
There were no other vehicles involved in this incident according to the police.
The roadway was closed for around six-and-a-half hours to allow a full collision investigation to be carried out at the scene of the accident.
Police are urging anyone who saw the vehicle prior to the accident or who witnessed the collision to cotact them immediately.
Sergeant Andy Gibb of the Road Policing Unit based in Dalkeith said: “This is an extremely tragic incident and our thoughts are today with the family of the woman who sadly passed away.
“Our enquiries into this collision are ongoing as we look to establish the full set of circumstances.”
He added: “I would urge anyone who was travelling in the area and who remembers seeing the vehicle prior to the collision to please contact police on 101 if they have not already done so.”