Hash chains are widely used for entity authentication or data-origin authentication. However, finite length of a hash chain limits its implementations. A new kind of hash chain, called self-renewable hash chain (SRHC) is proposed, which achieves a hash chain self-renewing or re-initialization smoothly, securely throughout its usage. The renewing process of SRHC does not need additional protocols or independent re-initialization processes and can be continued indefinitely to give rise to an infinite length hash chain. It also enhances security properties for conventional hash chain: fine-authentication and proactive updating etc. An application of SRHC - an improved 4-way protocol with SRHC for WLAN is presented that shows SRHC is available and practical.