In wireless sensor networks (WSNs), time synchronization is basically required to provide time-stamp for the reported events, active-sleep MAC protocols to extend network lifetime, etc. Most synchronization schemes assume that the send time of a packet is captured when packet transmission is just started, and the packet is modified to save the send time before packet transmission is not complete. However, it is difficult for system-performance limited sensor nodes to complete the packet modification in time. In this paper, we propose a synchronization scheme avoiding modification of the outgoing packet (SAMOP) based on the CSMA-CA protocol, where a transmitter and a receiver measure only time instance for the packet with their own local clocks and then a transmitter transfers the time measurements with a subsequent packet. Based on multiple time measurements, SAMOP synchronizes local clocks of both nodes. Simulation results show our SAMOP provides improved accuracy with respect to a synchronizing period.