 The southern terminus of the route is at the New Jersey state line in Palisades, where it becomes County Route 501 (CR 501).The northern terminus is at an intersection with NY 303 in Orangeburg; however, according to the New York State Department of Transportation (NYSDOT), the route continued for another to the northwest of NY 303 until by 2017.NY 340 was assigned to part of its modern routing in the early 1930s and extended to its current length in the early 1940s.