Short-circuit faults close to each end of a transmission line are normally cleared with some time delay by the distance relay at the opposite end of that line. To reduce this time delay, the pilot relaying schemes use communication links. This paper presents a non-communication method that provides high-speed distance relaying over the entire transmission line length. Similar to conventional distance relays, the proposed method requires voltage and current signals at the relay location as well as the impedance parameters of the protected line as inputs. Accelerated sequential tripping (AST) for faults on the endsections of the line is achieved by using the signals measured from the fault inception to several cycles after the operation of the remote-end circuit breaker (ORCB). The results show that the use of post-ORCB signals would accurately yield the fault distance. Two indices for detecting three-and single-pole ORCB are proposed so as to fulfil the prerequisite for accurate fault distance estimation and generating a trip command, if needed. The proposed method is successfully validated by conducting more than 10000 simulation cases on the 39-bus test system using DIgSILENT PowerFactory.