A number of parties were interested in the sites, which have been trading under the name Arnold Clark since August 13.
Ian Grieve, managing director at Ian Grieve, said: “We had a review and looked at the levels of investment required and returns and decided it was time to move on. ”
The company has retained its Subaru and Isuzu franchises at Falkirk, which Grieve now plans to focus on and grow.
Arnold Clark has also begun work on its Stafford-based Motorstore used car superstore, due to be opened early next year. Arnold Clark was unavailable for comment.