Rinse the beef tenderloin and pat dry with paper towels. Cut into pieces 8–12 cm long and 2–3 cm wide.
Mix salt and ground black pepper. Rub the mixture evenly on both sides of each steak.
Heat vegetable oil over medium-high heat in a frying pan until very hot. Place steaks in the pan. For medium-rare with a pink center, fry 4 minutes on each side. For well-done, fry 5 minutes on each side.
Arrange the cooked steaks on plates. Add tkemali sauce if desired and serve with your preferred side dish.