A non-2PL and deadlock-free concurrency control method, called the Ascending Order Locking Protocol (AOLP), is proposed. Based on AOLP, a serializable and deadlock-free scheduler can be built and its correctness is proved. To show the merit of AOLP, 2PL and AOLP are evaluated mathematically on a factor called the "Average Lock Range" (ALR). The mathematical results indicate that the ALR for 2PL is the worst case of AOLP regardless of the access sequence of a 2PL-based transaction.