You need a minimum of £1 million (Dh5.9m) to bank there and will rub shoulders with some of the world's richest businessmen, entertainers and politicians.
Coutts, the British private bank, often touted as the Queen's bankers, has expanded its presence in the Middle East with a new office at the Dubai International Financial Centre (DIFC).
The fact that one of the world's oldest banks has set up shop at one of the world's newest financial centres is a signal of how a bank with a 320-year history has thrust itself into the 21st century.
While a new customer may not bump into the Queen anytime soon - much of the interaction between a Coutts banker and a wealthy client takes place in the home - they will join an institution rich in tradition that has survived a series of global financial catastrophes.
And it's this international recognition of the brand's longevity and heritage that its chief executive, Rory Tapner, believes makes it so attractive to new clients here.
"Some of the royal associations with this brand probably help in this marketplace," he says. "The Middle East goes to London every summer and they want to bank with the most upmarket bank they can find in London."
With the Middle East now one of its five core markets - Coutts is downsizing operations from 177 nations to 50 to grow the international business more efficiently - it is a far cry from its early days in 1692 when John Campbell, a Scottish goldsmith, set up operations in The Strand in London.
Just as we have neon signs above shops today, he had a sign of Three Crowns with his initials above his establishment to signal his presence - a badge used right up until last year when Coutts dropped Campbell's initials from the logo.
As well as supplying plate and jewellery, Campbell made collars and badges for Queen Anne and also offered a comprehensive banking service with dukes as his customers.
The bank really established itself as the custodian of great fortunes two generations down the line when James Coutts, an Edinburgh merchant, married the founder's granddaughter in 1755. He later joined the bank and took on his younger brother Thomas as junior partner.
It was Thomas who attracted the first royal customer, bringing in George III's privy purse account - the UK government funding for the royal family.
"Thomas Coutts himself was a frightful snob and wanted to establish himself in London," explains the bank's chairman, the Earl of Home.
"He was quite sycophantic with the court and sat around as one might at the majlis here to be near the seats of power and eventually got to the king, George III. That's when he began to spread his wings and become the banker for significant people in the country."
By the time the bank was inherited by his 24-year-old granddaughter Angela Burdett in 1837 it was an established part of upper class society.
While Angela took the Coutts name, she was not permitted to run the bank - instead focusing her efforts on philanthropy, working with Charles Dickens on projects linked to poverty, health care and child welfare.
These themes are being readopted by Coutts, a bank with a strong philanthropic element in its DNA thanks to Angela's work, but on a more global scale.
"Almost every client we speak to, there will be this conversation about the value of money, responsibility around it and also what we can do in the philanthropic world," Tapner says.
The Coutts family were part of the brand's structure until the late 1990s and while the bank of today, part of Royal Bank of Scotland since 2000, no longer courts the landed gentry - probably because much of their wealth has been diminished - its association with the wealthy continues.
"If you look at the growth in the business, it's really the entrepreneurs, the entertainers, sportsmen and highly paid executives," says Tapner. "The mix of the business has changed from Thomas Coutts' era to something that is much closer to the current entrepreneurial wealth-generating group." Coutts is also one of three financial institutions recommended to winners of the UK's national lottery that can see people transformed into multimillionaires overnight.
"If you've never had any money and you've suddenly got £100m pounds, you need advice immediately because £100m can become £80m and then £70m very fast if you don't know what you are doing. Why do they come to us? Because that's precisely the type of client we like - somebody who may not understand how to think about wealth," says Tapner.
It's curious to think of the pop stars and footballers, who dominate news headlines, having a relationship with an institution so riddled in tradition - but Tapner says it is exactly this tradition that attracts clients because Coutts are experts in preserving wealth.
"The history is very important to us because the bank has in its DNA the ability to look after special people. If you are of immense influence or wealth, you don't want someone who is fazed by dealing with somebody who might have HRH or prime minister in front of their name.
"On the other side, customers in the banking industry like heritage; they like the fact you've been there and haven't got into trouble and I don't think Coutts has got into trouble in 320 years."
The bank did come into the firing line recently with two sizeable fines: one of £6.3m in November 2011 for the way it sold bonds to clients, and the second for £8.75m earlier this year for failing to monitor whether money it was handling was the proceeds of crime.
Tapner is quick to point out that the Financial Services Authority never found any actual wrongdoing, only that the processes the bank was using weren't stringent enough.
It was a tiny dent in Coutts' otherwise untarnished armour and the bank has taken great strides to update its procedures to avoid mistakes happening again and ensure it successfully merges its heritage with the modern world.
Recent changes include a single operating system for its entire UK and international network - a banking first - and revamping the logo.
There is also more focus on expanding its international client base. Although the bank first initiated a presence here 13 years ago, this year has seen investment into the new DIFC office and extra staff hired for its Abu Dhabi and Doha bases.
Tapner distances himself from the notion that Dubai is the regional headquarters, insisting it was chosen to house staff because of the DIFC's infrastructure and the security that comes with its regulator, the Dubai Financial Services Authority.
Rather, bankers typically service their clients' needs in their homes.
"When you go into the home you understand the family dynamic a bit better and it immediately leads into how the partner's finances are handled, and whether the client has thought about succession planning with their children," Tapner says.
So who is the typical Middle Eastern client?
Interestingly, unlike the UK market where customers have between £1 million and £75m, the capital-rich Middle East market starts and ends at a higher level simply because people in this region are richer.
Amir Sadr, co-head of Coutts Middle East, says a typical customer could be an entrepreneur who has accumulated a significant amount of wealth very quickly or a wealthy family running a local business.
How this relationship with the Middle East will evolve is unknown, but if those clients do step into the Dubai office, they will get a taste of the bank's history through its heritage wall in the entrance and a replica of hand-painted Chinese wallpaper given to Thomas Coutts in 1794 in the meeting room.
It may be no match for the Strand's historic archives, which includes cheques written by some of Britain's most prominent historical figures and a note from Thomas Coutts that reads: "I lent the king 50 crowns and I don't expect to see it back", but it hints at the bank's incredible story.
What is clear is that the Coutts name will become synonymous with the upper echelons of UAE society.
Last week the bank hosted the prestigious Coutts Polo at the Palace event that saw 1,000 of the capital's leading figures gather at Emirates Palace to watch polo - another British institution.
As Edward Hobart, the UK consul general for Dubai, said at the DIFC office opening last week: "You can't get more British than Coutts."
Whether Coutts really is the Queen's banker is not something Coutts will officially comment on.
"We tend to comment on people that have been dead for 100 years," Tapner says.
We will just have wait another century to find out for sure.
Alice Haine is a senior features writer for The National