In the aftermath of the financial crisis, the Royal Bank of Scotland ran an advertising campaign featuring customers standing in front of bucolic landscapes and talking about their careers and aspirations.

The adverts boasted of how many of the bank's branches were open at weekends and the tagline was "The Royal Bank of Scotland is here for you". It was part of a campaign by the bank to regain public trust, as was the promise in 2010 that it would not close down a branch if it was the last bank in town.

With the announcement yesterday that RBS is to close 44 of its branches - 10 in Scotland - that promise has now been broken. The boasts in the adverts about branches being open "from Sauchiehall Street to Stornoway" also sound hollow, particularly as the axed branches stretch from the Borders to Caithness and include at least one that is the last bank in town.

In defending the closures, RBS said yesterday the nature of banking had changed and the truth of that should be acknowledged. More customers are banking in more flexible ways and the pace of change has been accelerating in recent years. In 2007, less than one-third of Scots used the internet to do their banking; last year, it was half.

RBS cannot ignore this trend, which has led to falls in the number of customers going into branches (there has been a 30% drop in branch transactions since 2010) but it also has to recognise - particularly in light of its status as an institution that was bailed out by taxpayers - that it has responsibilities to the communities it serves.

Many of those communities will be worse off today thanks to the closures - communities such as Castletown in Caithness which will lose its only bank. For many Castletown residents who bank online, this will not be a problem, but then not everyone is in this situation. And closing branches will hit some small businesses hard as many of them still frequently use their local branches every week.

As Rob Gibson, the MSP who represents Castletown, points out, closing a branch in a rural area can also affect rural residents disproportionately because of the lack of good broadband connections. Even if it is true that banking has been changing in recent years, the availability of broadband should be a factor banks take into account in deciding which branches they are going to close. To fail to do so will leave the impression that rural areas are being singled out.

In years to come, it is probably inevitable more branches will close, but RBS and other banks must explore ways in which they can maintain a presence in towns and villages. Ross McEwan, RBS chief executive, has said he wants more automated tellers and cash machines in shops and railway stations, and that is a good idea. The mobile vehicle banking service has also been a success and should be expanded as much as possible.

RBS says it has a responsibility to adapt to what customers want, but that cannot mean only customers who bank online. A bank must aim to serve all its customers in the best way possible: urban and rural, young and old, those who use the internet and those who do not.