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Estimating channel state information (CSI) in the fast fading conditions is very challenging. In this study, a simple structure for cooperative diversity in decode-and-forward mode is examined, in which the transmitter, the relay and the receiver do not know the CSI. In this scheme, transmission of information is done in a two-phase process. In the first phase, differential modulated signals are radiated from the source. After decoding the received signal in the relay, the source and the relay collectively send information using differential space-time codes. A closed-form optimum power allocation in the sense of minimising pairwise error probability (PEP) for high signal-to-noise ratio (SNR) scenarios has been obtained. An interesting property of the optimum point is that it is independent of the channel statistics and the position of the relay, which improves its feasibility in the future communication systems. Numerical simulations verify the analytical results.