A new scheme to verifiably redistribute a secret from the old to new shareholders without reconstruction of the secret is presented in this paper. The scheme allows redistribution between different access structures and between different threshold schemes. A point worth mentioning is that this verifiable secret redistribution (VSR)scheme can identify dishonest old shareholders during redistribution without any assumption. A certain technique is adopted to verify the correctness of the old shares of the secret. As a result, the scheme is very efficient. It can be applied to proactive secret sharing (PSS) schemes to construct more flexible and practical proactive secret sharing schemes.