This paper considers channel-unaware two-way relay networks in which two single-antenna nodes exchange information via multiple non-regenerative relays, each with multiple antennas. A novel self-interference cancellation scheme for distributed differential space-time signalling is developed. Despite the absence of channel-state information, this scheme enables self-interference to be completely eliminated, thereby maximizing the signal-to-interference-plus-noise-ratio of the nodes. First, we obtain a lower bound on the pairwise error probability (PEP) under residual self-interference and we show that this bound approaches a non-zero constant at high signal-to-noise ratios (SNRs), indicating a zero diversity order and an asymptotic error floor. Second, we derive a necessary and sufficient condition for the proposed scheme to eliminate self-interference perfectly. Proper operation of this scheme requires the relays to have an even number of active antennas and for relays with odd number of active antennas, such a scheme does not exist. Third, we show that, when self-interference is cancelled perfectly, the error floor vanishes and an upper bound on the PEP approaches zero at high SNRs. In this case, it is shown that the diversity gain is equal to the number of relays and is independent of the number of antennas per relay. Finally, it is shown that the coding gain increases with increasing the number of antennas per relay and converges to a constant as the number of relay antennas becomes large.