The present invention relates to a computer-based electronic payment system comprising a payer's check issuing computer (100, 100A) for issuing an electronic check, a payee's check processing computer (200, 200A) for receiving and processing the electronic check from the payee's check issuing computer (100, 100A) and transmitting each accepted electronic check; and a transaction executing computer (300, 300A) for receiving and processing the electronic check transmitted from the payee's check transmitted from the payee's check processing computer (200, 200A). The electronic check issued by the payee's check issuing computer (100, 100A) also has an issue time data indicating a time of issue of the electronic check. The payee's processing computer (200, 200A) records a check identifier of each electronic check being accepted by the payee's check processing computer (200, 200A) during a first prescribed period of time and refuses an acceptance of the received electronic check in case a time of issue is older than the first prescribed period of time or the check identifier is identical to any recorded check identifier of an already accepted electronic check. To the contrary, it accepts the received electronic check when the acceptance is not refused.