In this paper, we propose a FBMC (filter bank multicarrier) duplexing scheme, where downlink and uplink use FBMC for their transmission. Downlink and uplink transmit at the same time and in the same frequency band but with different subcarriers. We then analyze the advantages and problems of the scheme. We show that it is impossible to achieve full synchronization in time and frequency with both downlink and uplink signals. Thus the synchronization errors will destroy the orthogonality between the downlink and uplink. It is shown that the synchronization errors cause the OFDM (orthogonal frequency division multiplexing) duplexing to be unreliable, while FBMC duplexing with proper prototype filter is very robust to such errors. An additional advantage of FBMC duplexing is the reduced number of null subcarriers required to control the out-of-band emission. The distinguished advantages make FBMC duplexing a better choice in applications like small cell, spectrum sharing, spectrum refarming and cognitive radio. Some problems are pointed out, which include high peak to average power ratio (PAPR), large dynamic range, and requirement for high resolution analog to digital converter (ADC). Simulations at various situations are shown to verify the results.