On July 17, 2006, at 1606 eastern daylight time, a Dassault Aviation, Mystere Falcon 900, N699BG, registered to and operated by Erg Aviation II Incorporated, as a 14 CFR Part 91 business flight, overran runway 1 during landing, and was stopped by the Engineered Materials Arresting System (EMAS), at the Greenville Downtown Airport, Greenville, South Carolina. The airplane was not damaged. Visual meteorological conditions prevailed and an instrument flight rules flight plan was filed. The airline transport-rated pilot, commercial-rated co-pilot, and three passengers were not injured. The flight departed Concord Regional Airport, Concord, North Carolina, at 1540. The pilot stated that the enroute phase of the flight was uneventful, and that he was cleared for a visual approach to runway 1. He said that during the final approach the anti-skid system test required a second test to receive the correct indication. Upon touch down, the co-pilot deployed the spoilers and thrust reverser. When the wheel brakes were applied the airplane began to drift to the left side of the centerline. The pilot indicated that the wheel brakes did not appear to be effective, however he was able to maintain directional control of the airplane. The airplane slowed down, overran the runway, and was stopped by the EMAS. Examination of the runway by an FAA inspector revealed that there were heavy black skid marks from the left main landing gear and the nose landing gear tires. There were faint black tire marks from the right main landing gear. The landing gear marks were visible from "taxiway J" to the end of the runway (overrun area) EMAS. The distance from taxiway J to the runway threshold is approximately 1,000 feet. In accordance with AMM MP32-122 and MP32-211 inspections were performed on the landing gear of the aircraft to determine if any deformity of the landing gear installation occurred. No discrepancies in wheel parallelism, camber angle, or caster angle were discovered. Additionally a complete functional test of the landing gear assembly and doors in accordance with AMM MP32-300, and no discrepancies were discovered. A functional test of the landing gear system was conducted in the ground and flight configuration. During the in-flight functional test a malfunction in the right main landing gear brakes anti-skid system occurred. The anti-skid system was removed in accordance with Dassault AMM MP32-404, and a functional test of the system was performed. During the test the components of the anti-skid system were examined, and the SPAD (Advanced Anti-Skid System) controller P/N C20188102, S/N M091 was found to be the origination of the brake failure. The SPAD controller was replaced and another functional test was performed. The anti-skid system passed all functional tests in accordance with MP32-404 for correct operation and the airplane was returned to service.