In 1772, nine years after work on the North Bridge began,  Sir Laurence Dundas of Kerse, for many years Member of Parliament for Edinburgh, started to build Dundas House on the east side of St Andrew Square. 

The house was designed by William Chambers and built of Ravelston Stone.  It was modelled on the Palladian villa of Marble Hill in Twickenham.

The house occupies a prominent position on the east side of St Andrew Square, set back from the square behind its own garden.

Following the death of Dundas in 1781, the house was sold to the government and subsequently became the principal office of the Excise in Scotland.  The Excise Office later moved to Drummond Place.

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In 1804, a 2-storey extension was added on the south side of the building.

In 1825, Dundas House was purchased by Royal Bank of Scotland, and in 1828 it became the bank's Head Office.  A new banking hall with a large domed ceiling and figures representing Commerce, Agriculture, Navigation and the Arts was added.  This hall opened in 1861 and is still in use today, looking very impressive following refurbishment in 1989.