We provide symbol-error-rate (SER) performance analysis for a multi-node wireless network employing a decode-and-forward cooperation strategy. An approximate expression for the SER of an N relay network with M-ary phase-shift-keying (M-PSK) signalling is derived at high enough signal-to-noise ratio (SNR). The approximation hinges on ignoring terms in the SER which are of order higher than (N+1) in the SNR. The validity of the derived approximate SER is justified through computer simulations for networks with different numbers of relays. The simulation results show that the approximation is tight at high SNR and that the cooperation protocol can achieve full diversity order equal to the number of cooperating terminals.