An Optical Line Terminal (OLT) needs to find and register newly connected Optical Network Units (ONUs) in the proposed Ethernet Optical Switched Access Network (E-OSAN) as well as the Ethernet Passive Optical Network (E-PON). In this discovery process, OLT measures round trip time (RTT) between OLT and each ONU and then assigns a Logical Link Identification (LLID) to each ONU. For E-OSAN, the conventional discovery method takes up to N discovery periods for OLT to register all ONUs, where N denotes the number of switch ports of the Optical Switching Module (OSM). This paper proposes an efficient method that completes discovery in just one period. This paper also evaluates the maximum ranging completion time of the proposed discovery method in a comparison with E-PON.