A biocompatible, self-supporting, curved, collagen membrane adapted to be secured by bone tacks or bone screws over exposed bone at a desired bone graft site in the alveolar ridge of a patient such that the membrane defines a space having a predetermined height and width over the exposed bone, in which the membrane maintains its structural integrity for at least 4 months after implantation at the bone graft site and then naturally breaks down and is resorbed by the patient's body, a method of making such a membrane, and a method of using such a membrane for vertical augmentation of the alveolar ridge of the patient.