The Dassault Aviation Falcon 900EX, crewed by two airline transport rated pilots, and accompanied by four passengers, had departed Boeing Field, Seattle, Washington, en route to Honolulu International airport, Honolulu, Hawaii. The aircraft climbed to FL 340 and was then cleared to FL 360 as it progressed along airway A332. As the flight proceeded, it encountered intermittent light to occasionally moderate turbulence and the crew made repeated requests for a higher altitude through Air Traffic Control, but the requests were not approved. A little more than half way into the flight, the aircraft’s track began to converge obliquely with a cold frontal system extending southwest through the Hawaiian Islands, and the aircraft encountered headwinds of more than 100 knots approximately 30 degrees right of the aircraft’s track. Approximately 4 hours 17 minutes into the flight, the aircraft was operating in the tops of clouds with good visibility when a passenger and her attendant left their seats to use the lavatory located in the rear of the aircraft. During this time the aircraft encountered moderate turbulence for a period of ten seconds or less and the attendant sustained a fractured ankle. Immediately following the event the crew requested and received approval for a climb to FL 370. Probable Cause: The aircraft’s encounter with moderate turbulence in cruise.