This dance is so-named because it emphasizes the essential character of the saltire; it uses only the basic 2-bar element of the figure, repeated six times, starting and finishing with the dancers in the "textbook" positions.

A saltire, Saint Andrew's Cross, is a heraldic symbol in the form of a diagonal cross or letter ex (X). Saint Andrew is said to have been martyred on just such a cross.

The Flag of Scotland, also known as the Saint Andrew's Cross or more commonly The Saltire (because it has the form of a saltire), is the national flag of Scotland. As the national flag, the Saltire differs from the Royal Standard of Scotland in that it is the Saltire which is the correct flag for all individuals and corporate bodies to fly in order to demonstrate both their loyalty and Scottish nationality. It is also, where possible, flown from Scottish Government buildings every day from 8am until sunset, with certain exceptions. 

(Source: <<http://www.scottish-country-dancing-dictionary.com/dance-crib/unsullied-saltire.html|Scottish Country Dancing Dictionary>>)