Nutritional supplements and methods for maintaining and/or improving the condition of bones or cartilage in a mammal, particularly a human. One such supplement comprises demineralized bone matrix (DBM) wherein the DBM comprises a bone growth improving amount of at least one osteoinductive growth factor. A preferred supplement composition further comprises at least one vitamin, such as vitamin E. One method comprises orally administering to the mammal on a periodic basis a supplement comprising DBM. In a preferred method the DBM composition is periodically administered and there is a further periodic administration of a therapeutically effective amount of a calcium-containing composition; the calcium-containing composition is administered temporally spaced apart from said DBM composition for maximum effectiveness.