Score meat by making shallow, diagonal cuts at 1-inch intervals across the steak; repeat on the other side. Place meat in a plastic bag that's set in a shallow dish.

In a medium mixing bowl, combine green onion, water, red wine, soy sauce, lemon juice, oil, dill, Worcestershire, garlic, celery seed and pepper. Pour over steak; seal bag. Marinate in the refrigerator for 6 to 24 hours, turning the bag occasionally to distribute the marinade. Drain meat, reserving marinade.

To Grill steak, place directly over medium coals for 12 to 14 minutes, or until it reaches desired doneness, turning once and brushing occasionally with the reserved marinade. To broil steak, place the meat on the unheated rack of a broiler pan about 6 inches from heat; cook 12 to 14 minutes or until it reaches desired doneness, turning once and brushing occasionally with reserved marinade.

To serve, use sharp knife to thinly slice meat across the grain.