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KY 359 begins at an intersection with U.S. Route 60 (US 60) in the northeastern part of Morganfield, within Union County. It travels to the northeast and leaves the city. It crosses over and and then intersects KY 141. It passes Highland Cemetery just before it begins a one-block concurrency with . Then, the highway curves to the north-northeast. It curves back to the northeast and crosses over . Just over 500 feet (150 m) later, it intersects the northern terminus of . Just under 0.5 miles (0.80 km) later is an intersection with the eastern terminus of KY 360. It then crosses over . The highway curves to the east-northeast and enters Henderson County.[1] KY 359 curves back to the northeast and crosses over an unnamed stream. It passes Smith Mills Cemetery before it enters Smith Mills. There, it meets its northern terminus, an intersection with KY 136 (Alzey–Mt. Vernon Road).[2]