We improve a secret sharing scheme, which enables users select their personal keys by themselves instead of being distributed by group manager and users can reuse their personal keys no matter the shared secret is renewed or recovered. Then we apply it to design a self-healing key distribution scheme. The new scheme achieves good properties. Firstly, the scheme reduces storage overhead of personal key to a constant. Secondly, the scheme conceals the requirement of a secure channel in setup step. Finally, the long-lived scheme is much more efficient than those in previous schemes.