Hash Chains are widely used in various cryptography applications such as one-time passwords, server-supported signatures and micropayments etc. However, the finite length (‘limited-link') of hash chains limits their applications. Some methods of re-initializing hash chains or infinite hash chains introduced in literatures are inefficient and un-smooth. In this paper, a novel scheme (a new kind of hash chain) is proposed, which re-initializes or updates by itself, named Self-Updating Hash Chain – SUHC. Highlights of SUHC are self-updating, fine-authentication and proactive updating. The updating process of SUHC is smooth, secure and efficient and does not need additional protocols or an independent re-initialization process, and can be continued indefinitely to give rise to an infinite length hash chain. An improved Server-Supported Signature with SUHC is also presented to show the application of SUHC.