In this paper, we analyze the outage probability of space-time network coding (STNC) in a distributed cooperative relaying system, where multiple sources transmit their information to a common destination with the help of multiple decode-and-forward (DF) relays in time-division multiple-access (TDMA) mode. We first derive an exact closed-form expression of the outage probability for STNC with an arbitrary number of relays for independent but not necessarily identically distributed (i.n.i.d.) Rayleigh fading channels. With the developed result, we discuss the impact of the transmit SNR, the outage threshold, the number of relays, the nonorthogonal codes, and the relay position on the system performance.