Brush steak with Worcestershire and marinate 15 minutes.
Lightly pat steaks dry and season well with salt.
Heat 1/2 tablespoon of oil in each of 2 (12-inch) nonstick or heavy skillets over moderately high heat until hot but not smoking, then saute steaks in batches, without crowding, 3 minutes on each side for medium-rare.
Transfer steaks to a platter and let stand, loosely covered, 5 minutes.