A spokesman said the closure was part of a wider plan of "simplifying the business", which has already seen the closure of about 40 branches in the UK.
He said the branch handled Â£400m from 16,000 customers, with 6,000 in Guernsey and 2,000 to 3,000 in Jersey.
The spokesman said a factor in the decision was the high cost of operating in an offshore banking centre.
The branch is the only one in the Channel Islands.
He said account holders would be contacted directly over the next few days to outline what he described as the "next steps", but customers should not be concerned and mortgages would continue to be honoured.
The company would look to find room for its employees elsewhere in its business, the spokesman added.

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The former England defender suffered a heart attack at Tottenham Hotspur's training centre on Thursday.
Ehiogu only spent a year with Rangers at the tail-end of his career.
But Thomson told BBC Scotland: "He will never be forgotten by the Rangers fans and I see a lot on social media - they think very highly of him."
Ehiogu, who won four caps for his country, was signed for Rangers by Walter Smith in January 2007 after being released by Middlesbrough following a seven-year spell at the Riverside.
Smith had taken over that month from Paul le Guen, whose side were trailing eventual champions Celtic.
Ehiogu partnered fellow veteran David Weir at the heart of the defence but lost his starting the place the following season and was released six months before the end of his 18-month contract.
However, Thomson thinks Ehiogu was instrumental in establishing the base that helped Rangers regain the Scottish title a few months after his departure.
"It was a turning point in Rangers' history when Walter came in and tried to change the team and steady the ship," said the former Scotland midfielder.
"And big Ugo and Davie Weir were fundamental to that swinging of the momentum."
Ehiogu only scored once for Rangers, but his decider in a 1-0 victory over Celtic in March 2007 was voted goal of the season by the club's fans.
"It was a special goal and probably one you would never expect from Ugo - an acrobatic overhead kick," said Thomson.
"I still picture him standing on the stage receiving his goal of the season award and all suited and booted to an amazing round of applause."
Thomson himself later joined Middlesbrough and discovered that Ehiogu, who suffered a heart attack at Tottenham Hotspur's training ground, had left a lasting impression with staff members there too.
"He was a lovely fella and, although I never knew him that well, I only spent five or six months with him, he was a true gent and he was everything you would expect in a true professional who had played at the very highest level," said the former midfielder.
"We both used to like a steam room after the game and I used to nip his ear and ask for advice on different things on and off the field and he was one of those boys, a bit like Davie, who welcomed giving you as much advice as possible."
Weir, who also played and coached against Ehiogu in England, echoed his former team-mate's sentiments.
"I'm devastated with the news and still in shock," Nottingham Forest assistant boss Weir told BBC Scotland.
"I'm sure as time goes on that goal (against Celtic) will be the abiding memory of Ugo at Rangers but I remember him more just as a nice guy to be honest.
"He was giant of a man but really gentle as a personality.
"He was a fantastic player - I think he had 400 odd games in the English Premier League and you don't do that easily."
In an official website statement, Rangers said the club was "shocked and saddened" by Ehiogu's death.
"The 44-year-old Englishman joined the Light Blues when Walter Smith returned as manager in 2007 and made a huge impact in his short time in Glasgow - notably his winning goal at Celtic Park in the derby," they added.
The Guernsey branch of the Co-operative Bank is to close early next year with the loss of 11 jobs.
[NEXT_CONCEPT]
Ugo Ehiogu, who has died at the age of 44, will be forever remembered fondly by Rangers fans, according to former Ibrox team-mate Kevin Thomson.