In wireless sensor networks, self-healing key-distribution schemes are used to ensure that, even if the message packets that are broadcast in some sessions get lost, the group nodes can still recover the lost session keys simply by using their personal secret keys and broadcast messages that have been received without requesting additional transmissions from the group manager. These schemes reduce network traffic, decrease the group manager's workload, and lower the risk of node exposure through traffic analysis. However, most existing schemes have many deficiencies, such as high overhead for storage and communication and collusion attacks. In this paper, we have proposed a modified, self-healing, key-distribution scheme based on one-way key chains and secret sharing. Our scheme has the properties of constant storage, lower communication overhead, long lifespan, forward secrecy, backward secrecy, and resistance to collusion attacks.