A (t, w) threshold scheme is a method for sharing a secret among w shareholders so that the collaboration of at least t shareholders is required in order to reconstruct the shared secret. This paper is concerned with the re-use of shares possessed by shareholders in threshold schemes. We propose a simple (t, w) threshold scheme based on the use of cryptographically strong pseudo-random functions and universal hash functions. A remarkable advantage of the scheme is that a shareholder can use a single string in the share of many different secrets; in particular, a shareholder need not be given a new share each time a new secret is to be shared