This is the ingredients for Science Diet Nature's Best Chicken & Brown Rice Adult Small Bites:
Chicken, Brown Rice, Whole Grain Wheat, Cracked Pearled Barley, Soybean Meal, Chicken Meal, Pork Fat (preserved with mixed tocopherols and citric acid), Dried Egg Product, Natural Flavor, Whole Grain Oats, Apples, Cranberries, Soybean Oil, Peas, Carrots, Dried Beet Pulp, Iodized Salt, Flaxseed, Broccoli, vitamins (L-Ascorbyl-2-Polyphosphate (source of vitamin C), Vitamin E Supplement, Niacin, Thiamine Mononitrate, Vitamin A Supplement, Calcium Pantothenate, Biotin, Vitamin B12 Supplement, Pyridoxine Hydrochloride, Riboflavin, Folic Acid, Vitamin D3 Supplement), Vitamin E Supplement, Choline Chloride, Taurine, Minerals (Ferrous Sulfate, Zinc Oxide, Copper Sulfate, Manganous Oxide, Calcium Iodate, Sodium Selenite), Preserved with Mixed Tocopherols and Citric Acid, Calcium Carbonate, Beta-Carotene, Rosemary Extract.
I found this from this link
Natural Dog Food Ingredients - Nature's Best Label just in case anyone is interested. I don't see any by-product except it says 'egg product' I don't know if that is similar to a by-product or not. Also there is no corn, either. Only thing bad I really see is the grains and soy products.