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Utilising the recently-developed unique factorisation of signals and distributed Alamouti coding, a distributed collaborative space-time block code design is presented for a two-way amplify-and-forward (AF) relaying network, where all nodes are equipped with a single antenna. Two asymptotic pairwise error probability (PEP) formulae are firstly derived for both fixed-gain AF and variable-gain AF over Rayleigh channels with the maximum-likelihood detector. Then, subject to the constraints on a fixed transmission bit rate and unity average transmission energy, the optimal constellation combinations with the optimal coefficients are attained by minimising the dominant term of PEP. It is shown that the PEP and the average block error rate of the newly-designed code are superior to those of the conventional distributed Alamouti code while the prior still has linear-decoding complexity.