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Consider a multi-relay cooperative diversity network consisting of a source, N relays, and a destination. For the transmission of a data symbol from the source to the destination, the relays cooperate with the source through the decode and forward protocol. All the links are statistically independent and undergo flat Rayleigh fading. Conventional instantaneous signal-to-noise ratio based selection combining at the destination chooses one link from the set consisting of the source-to-destination link and the N relay-to-destination links. However, this scheme does not account for the effect of the source-to-relay links in the error performance. To overcome this drawback, we present here a scaled selection combining scheme, which accounts for this effect through a deterministic scale factor. The end-to-end symbol error probability (SEP) of this scheme with binary phase-shift keying is derived in closed form. We also give a method of obtaining the optimum scale factor that minimizes the end-to-end SEP.