An Aronszajn line with no countryman suborders

Moore proved it is consistent assuming the existence of a supercompact cardinal that the class of uncountable linear orders has a five element basis.
The elements are X, w1, the dual of w1, C, and the dual of C, where X is any suborder of the reals of size w1, and C is any Countryman line.
This raises the question of the existence of an Aronszajn line with no countryman suborder, we will present such a construction by Moore from the combinatorial principle Mho.