In this paper, we investigate the outage performance of a multiuser threshold-based decode-and-forward integrated satellite-terrestrial relay network (ISTRN) with opportunistic user scheduling, where the satellite link and terrestrial links undergo Shadowed-Rician (SR) fading and correlated Rayleigh fading, respectively. First, we propose a new probability density function (PDF) to statistically characterize the square sum of independent and identically distributed SR random variables, which is more accurate and concise than existing expressions. Next, based on the new PDF, we derive an analytical expression of outage probability (OP) of the considered network. Furthermore, the asymptotic OP expression is developed at high signal-to-noise ratio to reveal the achievable diversity order of the considered ISTRN. Finally, computer simulation is conducted to validate the analytical results, and show the impact of various parameters on the outage performance.