During the three to five years prior to the menopause, the rate of bone loss increases. One way that physicians treat this is with oral contraceptive medication. However, the incidence of complications from oral contraceptives after the age of 40 increases. Therefore, a non-hormonal means of preventing bone loss should be useful. Fosamax (alendronate) is in a class of compounds called bisphosphonates. This study is being done to determine whether Fosamax can be used to prevent the increased rate of bone loss during the perimenopausal transition.