Key management has long been a challenging problem in distributed wireless sensor networks(DWSN) due to their high security requirements and strict resource constraints. Many schemes have been developed to establish keys in DWSN, including the famous EG scheme. Based on this classic scheme, this paper proposes a new key establishment and rekeying scheme: UEGS. The analysis in this paper demonstrates its feasibility, efficiency and security for key establishment and maintenance in DWSN.