In in-band full-duplex employing conventional frame structure, pilot contamination is inevitable due to asyn-chronism between the nodes. Asynchronism can occur for several reasons such as propagation delay and synchronization error. Pilot contamination increases channel estimation error for both the desired and self-interference channels. We propose a new frame structure that avoids interference during pilot transmission. The proposed frame structure utilizes maximum time offset information in order to cover all the possible time offsets. We then derive the mean square error (MSE) of the channel estimation when the proposed frame structure is employed. Furthermore, based on the MSE analysis, we deliver superior conditions for the proposed frame structure compared to the conventional one. Finally, we show that sacrificing pilot length to avoid interference during pilot transmission guarantees channel estimation performance when the power of the interference is large.