Ulster County is a county located in the U.S. state of New York. It is composed of four counties: Tyrone, Antrim, DOWN, and Monaghan. Tyrone is a six-letter county located in the northeast corner of Ulster County, while Antrim is a six-letter county located in the northwest corner of Ulster County. DOWN is a four-letter county located in the southeast corner of Ulster County, and Monaghan is an eight-letter county located in the southwest corner of Ulster County.