This paper analyzes the outage probability of space-time network coding (STNC) with amplify-and-forward (AF) relays in a cooperative relaying system, where multiple sources transmit their information to a common destination with the help of multiple AF relays in time-division multiple-access (TDMA) mode. We derive an approximate closed-form expression of the outage probability for STNC with an arbitrary number of AF relays for independent but not necessarily identically distributed (i.n.i.d.) Rayleigh fading channels. Numerical results validated our analysis. Moreover, with the developed result, we also discuss the impact of the transmit signal-to-noise ratio (SNR), the outage threshold, the number of relays and the nonorthogonal codes on the system performance.