Preheat barbecue grill. Combine juice, soy sauce, brown sugar, and cornstarch in 1-cup glass measure, mixing well. Microwave on full power (100%) 2 1/2 to 3 minutes or until thickened, stirring once.
Place beef steaks on grid over medium, ash-covered coals. Grill, uncovered, 11 to 14 minutes for medium rare to medium doneness, turning occasionally and brushing both sides with some of the glaze during last 5 minutes.
To broil, place steaks on rack in broiler pan so surface of beef is 3 to 4 inches from heat. Broil 14 to 18 minutes for medium rare to medium doneness, turning once and brushing with glaze during last 5 minutes.