It is understood the would-be robber threatened the manageress with a handgun.

The manageress was walking up to the Royal Bank of Scotland on Strathmartine Road, just north of the Kingsway, when the man sidled up to her and spoke to her briefly before demanding to be taken inside.

She screamed for help and the teacher ran to her aid, followed by another customer waiting for the bank to open.

The teacher then gave a statement to police at their Bell Street HQ, along with a local engineer who ran to her aid.

The armed robber walked away calmly but empty-handed and into a black 4x4, which did a U-turn and drove off north along Strathmartine Road.

Although badly shaken by the incident, the manageress was unhurt.

The would-be robber was around 6 ft, wearing a dark coat and dark trousers. He is thought to be in his 40s.

Police arrived on the scene shortly afterwards and stationed cars along the main arterial roads into Dundee in a bid to catch the robber.

One of the men who ran to the aid of the manageress was an engineer at Laing’s Domestic Appliances, and his van remains behind the police cordon at the bank.

Bill Gibson from the firm said, “I’ve not spoken to him, but from what I understand he chased the robber’s car.

“He’s now gone to Bell Street to give a statement.”

Neighbours living near the bank were alerted to the crime when they heard the manageress scream.

Martha Dorward (88), a regular customer at the branch, said, “My son said he heard someone screaming, and then a little while later I heard the screeching of car tyres.

“I use the branch probably about once a week, so I know the staff more or less. It’s just awful what’s happened — I think that’s the second time that branch has been robbed. I hope everyone is okay.”

Mrs Dorward’s son Ian (51) said, “I heard some screaming, and the commotion lasted until about 8.40 am.

“There have been police everywhere since then, but nobody really knows what happened.”

Kevin Vials, who lives opposite the RBS, added, “I left home around 8am and by the time I came back to pick up some materials for work at 9 am it had all happened.

“My wife is a teacher and left for school around eight, and my daughter went to school around half eight, so they might have seen something.

“There are always people outside the bank, but you don’t expect anything like this to happen.

“The bank has CCTV and my house gets picked up in it, so I’m sure they’ll be able to get a pretty good idea of what happened.”

Sharon Grant, who lives next door to the bank, said, “The first I knew of it was when I went to take my youngest to school and heard all the commotion.”

A spokesman for the Royal Bank of Scotland confirmed the Strathmartine Road branch had been due to open at 9.15 this morning, and added, “In circumstances such as this all inquiries are dealt with by local police.”

The police urge any motorists or pedestrians who were in the area around the time of the incident to contact them on 0845 600 5705.