This study is being conducted to compare the effect of increasing nasal teriparatide dosing on percent change in Bone Mineral Density (BMD) of the lumbar spine after 24 weeks of therapy in postmenopausal women with low bone mineral density.

Inclusion Criteria:

• Postmenopausal Female patients up to 89 years, inclusive;
• BMI ≤ 35 kg/m2, inclusive;
• In good health, determined by medical history and physical examination, as well as normal 12-lead ECG and vital signs;
• Females will be non-pregnant, non-lactating, and either post-menopausal for at least 1 year, surgically sterile (including tubal ligation, hysterectomy) for at least 3 months, until 30 days following Study Completion be willing to use an approved method of contraception;
• Have a minimum of two evaluable non-fractured lumbar vertebrae.
• Have low bone mineral density defined as having a T-score ≤ -2.0 as determined by DXA scan at either the lumbar spine (L1-L4) or total hip

Exclusion Criteria:

• Serious Medical Condition
• History of diseases which affect bone metabolism other than postmenopausal osteoporosis such as Paget's disease, any secondary causes of osteoporosis, hypoparathyroidism, or hyperparathyroidism
• Have a history of cancer within the past 5 years, except for basal cell carcinoma
• Have hypocalcemia or hypercalcemia from any cause or have a recent history of kidney stones or pre-existing hypercalciuria;
• Have used any of the mostly commonly prescribed osteoporosis medications within 3 months of starting the investigational product, or for more than 1 month at any time within 6 months prior to starting investigational product.