Non-linearities introduced by the power amplifier stage can significantly reduce the performance of self-interference cancellation in full-duplex transceivers. Accordingly, we propose a full-duplex system architecture that predistorts the digital baseband transmit signal to account for the non-linear memory effects of the power amplifier. Implementation results for a 5 MHz OFDM signal (operating with 20 dBm average transmit power) on a full-duplex testbed show that a further 13 dB suppression can be obtained, compared to the case when no predistortion is applied. The power levels of out-of-band emissions are also significantly reduced.