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In fading channels, increasing diversity gains can effectively improve the reliability of transmissions. This letter considers high-order diversity acquisition by incorporating signal space diversity (SSD) into a decode-and-forward (DF) cooperative system. Our focus is on the bit error probability (BEP) analysis for this cooperative system. In particular, a tight closed-form upper bound on the end-to-end BEP is derived. Moreover, an asymptotic approximation for the BEP is presented which reveals that both the signal space diversity and the spatial diversity gains are achieved when all channels are available. Simulation results validate the theoretical analysis and show that a significant BEP gain over the traditional DF-based system is obtained at no additional power or bandwidth expense.